UC-NRLF 


*C    3M    SOb 


•  •.-,." 


;  - 


m 


$p 

mi 


W*$  •«*£"-*  ••• -  Y ~'fe'i3'°:^$~''^ *j  ~ /srX" '^^- "•"•     ^^r/5^TO^P^'''---      ^^ir^"^^-'-^^  \^^^v''^^-" v^  J*  r**^r-   *A»' 

'^•^^^^^S^^f^^  $$lw$$S* '  SlW^iirfe  .^^^- f '')^b;  ^^b^^w'l 
.  ;^$^~f3fe$^  '^^^^"n&^lfe-^f ^/^ ; 


y.frMwr«*aF«Ki 
?o^^3*lr^^ 

'  ^Cln3)   JtkJtJp-  -<Zfr: .  °- 


ufSU^  ^^Tm5il^4^^l 


LIBRARY 

OK  THK 

UNIVERSITY  OF  CALIFORNIA. 


»w« 


§^?^^^?^^^^^^^^ 

XU/iy^V.o,./^^*:^  »*  />yw? '»*.:2^)  ^-^  *JL*  /»*>**    a^TzF^flOf  V*.  Sr^**i.-s«g^ 


'•^5^*  •    **•   \U(^  **b"t»  •./!(•    ^^r      "V^Alf^  **v-.rf  ZlKwi^f*'+  i^^Mi^  * 

jS^h^i^«sij^3*-5^te^^ji 

^^^^fe'^s^^lsl 


rY •'W^^i^s^' «o (^%  ^^^Z^^r^j^v^ 

%^^^¥^ilf*^ 

-'^>^^jjv^rOv-^  JflSfc  aJFfOSaWa 


S    V&  liiLjZ/^  ''ffif^"  ^*cr*'  i<~$k  i      A/5  ->*r*» C=s>'    D  ^St         JIA 

^^S>%  •  •*  i''  ^**  W  ^^>s>"  ^S^V^^TV»IW^^^V     •+ 

s^«te^eEE«wSrs^jg 


. 

-'' 


TABLES 


OF 


MELPOMENE, 


BY 


E.    SCHUBERT. 


COMPfTEI)    FOB    THE 


AMERICAN  EPHEMERIS  AND  NAUTICAL  ALMANAC, 


rNDER    THE   SUPERINTENDENCE    OF 


COMMANDER  CHARLES  HENRY  DAVIS,  U.  S.  N. 


UNIVERSITY 


BUREAU    OF    ORDNANCE   AND    HYDROGRAPHY, 
WASHINGTON. 

I860. 


CAMBRIDGE: 

ELECTROTYPED  AND  PRINTED  BY  WELCH,  BIGELOW,  &  CO., 
UNIVERSITY  PRESS. 


ASTRONOMY 
UBRARY 


TIVBESITY) 

/  J  VI  W. 

REPORT 


TO 


COMMANDER   C.    H.    DAVIS,  U.  8.  N. 


I.    ON  THE  COMPUTATION  OF  THE  GENERAL  PERTURBATIONS  OF  MELPOMENE 

BY  JUPITER. 

BY   ERNEST    SCHUBERT. 

FOB  the  computation  of  these  perturbations,  Professor  ENCKE'S  method,  published  in  the  Berliner  Jahrbuch 
for  1857,  lias  been  used  in  order  to  try  it  by  a  complete  application  to  a  special  case.     The  basis  of  the 
work  are  the  following  elements  :  — 

MELPOMENE.  JUPITER  (from  BOUVARD'S  Tables). 

1854,  Jan.  0,  Washington  Mean  Time  ;  (osculating).  1854,  Jan.  0,  Washington  Mean  Time. 

M  =  79  56  36".81  o     ,  ,  1                            M  =  269°  43'  39"1 

*    =  15  14  31.52)  M  E     £         n'    =  16  16  53.3)  n    =  11  58  43.2 

8  =  150     1     8.21 )  8'  =  19  16  43.7  [-^^^       Q  =  98  56  38.7 

i     =  10     9     4.77  »v     =  15  28  17.2)                       i     =  1  18  39.5 

<f    =  12  32  46.29  ,,    =  2  45  55.1 

H    =  1019".96852  p    =  299".12861 

loga=  0.3609465  log  a  =  0.7162370 

Tlie  plane  of  the  orbit  of  Melpomene  has  been  adopted  for  the  fundamental  plane,  and  the  major  axis  for 
i  he  line  of  the  abscissas.  The  orbit  of  Jupiter  is  referred  to  this  fundamental  plane  by  means  of  the  formulas 
on  page  390  (Jahrbuch  for  1857). 

Now  for  the  computation  of  -&-  the  periphery  was  divided  into  16  parts,  so  that  M  and  M  (the  mean 
anomalies  of  Melpomene  and  Jupiter)  for  those  16  points  are  0°,  22°.5,  45°,  &c.  Log  m>  «*  =  5.5760322  in 
units  of  the  seventh  decimal-place,  and  for  the  Julian  year  as  the  unit  of  time.  Each  point  of  the  Melpomene 
orbit  is  combined  with  all  1C  points  of  the  Jupiter  orbit,  which  gives  16  X  16  =  256  values  of  m  .  On 
page  854,  Professor  ENCKE  says  that  those  values  can  be  checked  only  by  double  calculation,  since  it  cannot 

be  done  by  the  differences  in  the  series  obtained  for  the  different  M.     But  I  found  that,  if  we  arrange  the 

m'  if 
quantities     <f  according  to  another  principle,  they  can  be  tested  by  differences,  which  will  be  shown  by  the 

following :  — 


-O    o  ' 


A. 

] 

S. 

M  = 

0° 

22°.5 

45° 

67°  .5 

90° 

etc. 

11776  2 

rn'it 
P™ 

11776.2 

9701.8 

M=0° 
5823.7 

3385.1 

2150.3 

3722.0 

7454.2 
6636.6 

11195.8 
10851.5 

7454.2 

11195.8 

M=22°.5 

10838.6 

7038.9 

4099.4 

1419.6 

2117.7 
2110.9 

3515.1 
3583.5 

6418.2 
6753.7 

11154.1 
12234.1 

3722.0 

6636.6 

M=45° 

10851.5 

12032.8 

8415.1 

' 

; 

; 

0                        o' 

O                     0 

2117.7 

3515.1 

M=  67°  .5 
6418.2 

11154.1 

13455.3 

22.5  &    0 
45      &  22.5 

0     &    0 
22.5  &  22.5 

1419.6 

2110.9 

3/=90° 
3583.5 

6753.7 

12234.1 

etc. 

Diff.  -  22.5 

Diff.  —     0 

etc. 

t 


•>  77." 


This  sketch  needs  no  further  explanation ;  the  principle  for  the  arrangement  in  B  from  A  is  very  simple, 

and  it  is  obvious  that  it  is  the  vertical  series  in  B  which  can  be  tested  by  differences. 

m'  if 
In  Table  A  the  values  of  — ^    are  functions  of  M,  and  they  are  developed  in  series  of  the  form, 

—t ~  =  a°  4-  a1  cosM     +  V  sin  M' 

4-  a"  cos  2  M  +  5"  sin  2  M. 

It  is  evident  that  now  in  these  series  the  coefficients  are  functions  of  M,  and  they  must  be  developed  in  series 
of  the  same  form,  that  is,  for  instance, 

a°  =  «°  +  a'  cos  M     +  /?'  sin  M 
-\-  a"  cos  2  M+  p"  sin  2  M 

Each  of  the  latter  series  must  be  multiplied  with  the  cos  f'  M1  or  sin  i1  M  belonging  to  it,  and  then,  finally, 

m!  if 
by  resolving  the  products  of  two  cosines  or  sines  into  sums  and  differences,  we  obtain  — ^-  developed  in  series 

of  the  general  form 

oj'  cos  (t  M—  i'  M)  +  ^  sin  (f  Jf  —  f'  jlf ). 

In  order  to  have  throughout  — t'  JM7  we  only  have  to  change  the  sign  of  t'  and  that  of  the  coefficient  of 
the  sine. 

The  formulas  for  the  components  of  the  disturbing  force  (page  392)  are  :  — 


z.  =  -'"•  {(?-?)*'•} 


m'  if 
Therefore,  after  having  developed  —  M    according  to  the  above  precepts,  we  subtract  from  it 


=  2684.3  -f  388.2  cos  M 

+  28.1  cos  2  M 
+  2.0  cos  3  M 
4-  0.1  cos  4  M 


and  pot  tliii*  m'  »'  (       —    ,  V     TliU  prriixliral   -<T\>--  i-  to  l>c  multipli<Ml  Muvosivcly  with  r',,  y\,  and 
developed  also  in  periodical  -i-rii--  tln-y  are:  — 

x',  =  —0.37409  +  5.16475  cos  AT     +  0.25210  sin  AT» 
+  0.12450  cos  2  JIT  +  0.00608  sin  2  JT 
+  0.00450  cos  3  M'  +  0.00022  sin  3  M1 
+  0.00019  oos  4  M' 

y,  =  -f-0.02313  —  0.31933  cos  AT     +  5.14340  sin  JIP 

—  0.00770  cos  2  M1  +  0.12401  sin  2  AT' 

—  0.00028  cos  8  if  +  0.00446  sin  3  M' 

+  0.00019  8in  4  M> 

*'l  ==  —0.03518  +  0.49698  cos  M>     +  0.68709  sin  Jf 
-j-  0.01336  ccw  2  Af  +  0.01657  sin  2  .¥' 
-j-  0.00185  cos  3  M'  +  0.00060  sin  3  Jf' 
|-  0.00 144  cos  4  M1 
+  0.00142  cos  5  M' 
+  0.00142  cos  6  M' 
+  0.001 42  cos  7  M' 
+  0.00071  cos  8  AT 

m'  if 

After  that,  the  periodical  series  -^j-  must  be  multiplied  with  — xt  and  y,. 


We  have 


•,  =  +0.74808  —  2.25537  cos  M 

—  0.24159  cos  2  M 

—  0.03886  cos  3  M 

—  0.00741  COB  4  M 
-  0.00155  cos  5  M 

—  0.00035  cos  6  M 


— y,  =  —  2.22785  sin  M 

—  0.23961  sin  2  Jf 

—  0.03861  sin  3  M 
-  0.00737  sin  4  M 

—  0.001 55  sin  5  M 

—  0.00035  sin  6  M 


Finally,  after  these  fire  multiplications,  by  forming  the  sums,  we  obtain  the  series  for  X,,  Y,,  Z,. 
I  subjoin  here  now  the  terms  tf-yf  and  of  m'  x'  („  —  -^J  retained  for  multiplication,  the  terms  smaller 
than  0.5  having  been  omittc.1. 


m? 

«• 

P 

a 

1.   f 

CM 

sin 

•',      •• 

CM 

sin 

«'.      f 

cos 

tin 

«,     f 

CO* 

•in 

0      0 

+434&S 

0.0 

-4    - 

-      7.3 

0.0 

6    -1 

+      5.6 

-    5.8 

-a  -2 

-      1.1 

+    0.6 

1       0 

-  MM 

•M 

-3    - 

+      6.3 

-    1.6 

7    -1 

-      2.7 

+    6.6 

-1    -2 

-    14.0 

-    8^ 

3      0 

+     19.8 

-60.9 

-8    - 

-      6.0 

+    2.H 

8    -1 

0.0 

-    3.7 

0    -2 

+  195.3 

+  33.7 

3       0 

-       1.3 

-  5.1 

-1    - 

+  109.0 

•   64.1 

1     -2 

-1174.9 

I.Mi.- 

4       0 

-  1.6 

0    - 

-1384.0 

+  90.2 

-8    -2 

0.0 

+    0.5 

a  -2 

+2618.4 

-301.3 

1    - 

.:.•_•,>-.» 

-305.3 

-7    -2 

-f      0.5 

-    1.1 

3    -2 

+  350.1 

-  13.4 

-S    -1 

0.0 

-  3.7 

9    - 

.    I-.-..-J 

-(•  26.4 

-6  -a 

-      C.8 

+    0.7 

4    -2 

+     77.3 

-  27.7 

-7    -1 

+      2.9 

+  6.7 

3    - 

+    48.1 

-  43.1 

-5    -2 

+      1.0 

-    0.5 

5    -2 

+    16.1 

-    8.6 

-€    -1 

-      54 

-  5.1 

4    - 

+    18.5 

-    7.9 

-4    -2 

-      1.2 

0.0 

6    -2 

+      4.7 

-     1.5 

-o    -1 

+      6.6 

+  3.9 

5    - 

-      4.4 

+    0.8 

-3    -2 

+      0.9 

+    0.5 

7    -2 

0.0 

-     1.7 

TO'*' 

p°" 

«,      i' 

cos 

•  sin 

.',      '•' 

cos 

sin 

.',     .'' 

cos 

sin 

••,  >•' 

cos 

sin 

8    -2 

0.0 

+     0.5 

-2    -4 

+      0.8 

+    1.1 

6    -5 

+     96.3 

-  21.5 

-5    -7 

+      5.3 

+    2.6 

-1     -4 

1.1 

•    1.8 

7    -5 

+     38.0 

-  11.8 

-4     -7 

7.4 

0,0 

-8    -3 

+      0.5 

+     1.2 

0    -4 

+      3.0 

+    3.7 

8    -5 

+      4.5 

1.2 

-3    -7 

+      6.8 

-     3.0 

-7    -3 

-      0.9 

-     2.9 

1     -4 

31.4 

-    5.3 

-2    -7 

5.3 

+    5.3 

-6    -3 

+      2.0 

+    2.1 

2    -4 

+  158.1 

-  19.3 

-8    -6 

+     12.7 

1.2 

-1     -7 

+      2.4 

-    G.7 

-5    -3 

2.8 

1.2 

3    -4 

-  447.7 

+120.2 

-7    -6 

+      4.4 

-    5.8 

0    -7 

0.0 

+     7.4 

-4    -3 

+      2.8 

0.0 

4     -4 

+  506.8 

-117.6 

-6    -6 

+      2.7 

0.0 

1     -7 

3.1 

6.5 

-3    -3 

-      2.9 

+    1.1 

5     -4 

+  181.6 

-  30.1 

-5    -6 

+      1.2 

-     1.0 

2    -7 

+      4.3 

+    5.1 

-2    -3 

+      1.8 

-    2.4 

6    -4 

+    52.8 

-  15.4 

-4    -6 

1.0 

0.0 

3    -7 

2.3 

-    2.7 

-1    -3 

0.0 

+    4.8 

7    -4 

+     14.7 

-    4.9 

-3    -6 

+      0.9 

0.0 

4    -7 

6.7 

+     4.7 

0    -3 

-    27.6 

-  12.0 

8    -4 

+      2.2 

1.6 

-2    -6 

1.1 

-    0.8 

5    -7 

+    33.9 

-  11.6 

1     -3 

+  202.1 

+    1.6 

-1    -6 

0.0 

+    1.0 

6    -7 

-    45.4 

+  23-5 

2    -3 

-  778.5 

+153.7 

-8    -5 

+      4.5 

1.2 

0    -6 

0.0 

1.0 

7    -7 

+    23.5 

-    2-9 

3    -3 

+1199.2 

-205.2 

-7    -5 

+      2.8 

-    4.0 

1    -6 

1.2 

+    0.8 

8    -7 

+      6.9 

-  10.9 

4    -3 

+  232.1 

-  30.9 

-6    -5 

+      2.6 

+     1.5 

2    -6 

+     .5.7 

0.0 

5    -3 

+    73.9 

-  21.2 

-5    -5 

-      2.5 

1.5 

3    -6 

-    22.5 

+    4.0 

-8    -8 

+      3.6 

0.0 

6    -3 

+    15.1 

-    5.3 

-4    -5 

+      2.9 

0.0 

4    -6 

+    68.9 

-  20.7 

-7    -8 

6.9 

-    8.9 

7    -3 

+      5.8 

-    4.7 

-3    -5 

2.8 

+     1.1 

5    -6 

-  116.8 

+  48.6 

-6    -8 

+     13.0 

+     3.8 

8    -3 

+      0.5 

+     1.2 

-2    -5 

+      1.9 

-    2.1 

6    -6 

+    75.3 

-  25.2 

-5    -8 

3.6 

-    2.4 

-1     -5 

1.3 

+    2.8 

T     —  D 

+    46.2 

-  18.2 

-4     -8 

+      1.9 

0.0 

-8    -4 

+      2.2 

-     1.6 

0    -5 

0.8 

-    3.2 

8    -6 

+     12.7 

1.2 

4    -8 

+      1.9 

0.0 

-7    -4 

0.0 

+    0.8 

1     -5 

+      5.7 

+    4.3 

5    -8 

3.6 

+    2.4 

-6    -4 

+      1.3 

1.2 

2    -5 

-    30.7 

1.1 

-8    -7 

+      6.9 

-  10.9 

6    -8 

+     13.0 

-    3.8 

-5    -4 

1.4 

+    0.6 

3    -5 

+  111.6 

-  23.4 

-7    -7 

+    24.3 

+    8.4 

7    -8 

6.9 

+    8.9 

-4     -4 

+      1.5 

0.0 

4     -5 

-  240.3 

+  80.8 

-6    -7 

6.4 

-    9.8 

8    -8 

+      3.6 

0.0 

-3    -4 

1.6 

-    0.6 

5    -5 

+  204.6 

-  59.9 

•"'(£-£) 

«•',     « 

cos 

sin 

i',      i 

cos 

sin 

>',      i 

cos 

sin 

«•',     i 

cos 

sin 

0       0 

+1663.9 

0.0 

6    -1 

-      1.2 

-    0.8 

-4    -3 

-      1.6 

-    0.6 

1     -4 

+     18.5 

+     7.9 

1       0 

-1772.6 

-  90.2 

7    -1 

3.1 

+    6.5 

-3    -3 

-      2.9 

+     1.1 

2    -4 

+     77.3 

+  27.7 

2       0 

+  167.2 

-  33.7 

-2    -3 

+      0.9 

+    0.5 

3    -4 

+  282.1 

+  30.9 

3       0 

-    29.6 

+  12.0 

-7    -2 

-      5.3 

+    5.3 

-1    -3 

+      6.3 

•     1.6 

4    -4 

+  506.8 

+117.6 

4       0 

+      2.9 

-    3.7 

-6    -2 

1.1 

-    0.8 

0    -3 

+      1.3 

+    5.1 

5    -4 

-  240.3 

-  80.8 

5       0 

-      0.8 

+    3.2 

-5    -2 

+      1.9 

-    2.1 

1    -3 

+    48.1 

+  43.1 

6    -4 

+    68.9 

+  20.7 

6       0 

0.0 

+     1.0 

-4    -2 

+      0.8 

+    1.1 

2    -3 

+  350.1 

+  13.4 

7    -4 

6.7 

-    4.7 

7       0 

0.0 

-    7.4 

-3    -2 

+      1.8 

-    2.4 

3    -3 

+1199.2 

+205.2 

8    -4 

+      1.9 

0.0 

-2    -2 

1.1 

+    0.5 

4     -3 

-  447.7 

-120.2 

-7    -1 

+      2.4 

-    6.7 

-1    -2 

6.0 

+    2.8 

5    -3 

+  111.6 

+  23.4 

-8    -5 

-      3.6 

-    2.4 

-6    -1 

0.0 

+     1.0 

0    -2 

+     19.8 

+  60.9 

6    -3 

-    22.5 

-    4.0 

-7    -5 

+      5.3 

+    2.6 

-5    -1 

1.3 

+    2.8 

1    -2 

+  185.2 

-  26.4 

7    -3 

2.3 

+    2.7 

-6    -5 

+      1.2 

1.0 

-4    -1 

1.1 

•    1.8 

2    -2 

+2618.4 

+301.3 

-5    -5 

-      2.5 

1.5 

-3    -1 

0.0 

+    4.8 

3    -2 

-  778.5 

-153.7 

-8    -4 

+      1.9 

0.0 

-4    -5 

1.4 

+    0.6 

-2    -1 

-    14.0 

-    8.8 

4     -2 

+  158.1 

+  19.3 

-7    -4 

7.4 

0.0 

-3    -5 

-      2.8 

-    1.2 

-1    -1 

+  109.0 

+  64.1 

5    -2 

-    30-7 

+     1.1 

-6    -4 

1.0 

0.0 

-2    -5 

+      1.0 

-    0.5 

0    -1 

-  602.6 

-  25.8 

6    -2 

+      5.7 

0.0 

-5    -4 

+      2.9 

0.0 

-1    -5 

+      6.6 

+    2.9 

1    -1 

+5208.0 

+305.3 

7    -2 

+      4-3 

-    5.1 

-4    -4 

+      1.5 

0.0 

0    -5 

0.0 

0.0 

2    -1 

-1174.9 

-156.8 

-3    -4 

+      2.8 

0.0 

1    -5 

4.4 

-    0.8 

3    -1 

+  202.1 

1.6 

-7    -3 

+      6.8 

-    3.0 

-2    -4 

1.2 

0.0 

2    -5 

+    16.1 

+    8.6 

4    -1 

-    31.4 

+    5.3 

-6    -3 

+      0.9 

0.0 

-1     -4 

7.3 

0.0 

3    -5 

+    73.9 

+  21.2 

5    -1 

+      5.7 

-    4.3 

-5    -3 

2.8 

+    1.1 

0     -4 

0.0 

+    1.6 

4    -5 

+  181.6 

+  30.1 

"(*-*) 

«',    1 

tin 

i'.      * 

cos 

sin 

•',      ' 

cos 

sin 

••',     i 

cos 

sin 

5    -5 

+  204.6 

a  -6 

+      4.7 

-     i.:. 

-1     -7 

+      2.9 

+    6.7 

-6 

-8 

+      4.5 

1.2 

6    -5 

-  116.8 

-  48.6 

3    -6 

+    l.">.i 

+    5.3 

0    -7 

0.0 

0.0 

-4 

-8 

+      2.2 

1.6 

7    -5 

+    33.9 

+  11.6 

4    -6 

+    58.8 

•    i:..4 

1     -7 

-      2.7 

6.6 

-3 

-8 

+      0.5 

+     1.2 

8    -5 

3.6 

•J.I 

5    -6 

+    96,3 

•  -ji.:> 

8    -7 

0.0 

+    1.7 

-2 

-8 

0.0 

+    ii.:. 

6    -6 

+    75.3 

•J.-..-J 

3    -7 

+      5.8 

+    4.7 

-1 

-8 

0.0 

-    3.7 

-8    -€ 

+     13.0 

+    3.8 

7    -6 

1"..! 

•j.:.;, 

4     -7 

+     14.7 

+    4.9 

0 

-8 

0.0 

0.0 

-7    -6 

6.4 

-    9.8 

8    -6 

+     13.0 

+    3.8 

6    -7 

+    38.0 

+  11.8 

1 

-8 

0.0      +    3.7 

-6    -6 

+      2.7 

0.0 

6    -7 

+    46.2 

+  18.2 

2 

-8 

0.0  i    -    0.5 

-5    -€ 

+      2.(i 

{JS 

-8    -7 

-      6.9 

-    8.9 

7    -7 

+    23.5 

+    8.9 

3 

-8 

+      0.5 

-    1.2 

-4    -€ 

+       1.3 

I.-J 

-7    -7 

+    84.3 

+    8.4 

8    -7 

6.9 

-    8.9 

4 

-8 

+       -'.•-' 

+    1.6 

-3    -6 

+       2.0 

+    2.1 

-€    -7 

+      4.4 

-    6.8 

5 

-8 

+      4.5      +     1.2 

-2    -6 

0.8 

+    0.7 

-5    -7 

+      8.8 

-    4.0 

-8    -9 

+      3.6 

0.0 

6 

-8 

+     12.7      +     1.2 

-I    -6 

5.1 

-4    -7 

0.0 

+    0.8 

-7    -8 

+      6.9 

-  10.9 

7 

-8 

+      6.9      +  10.9 

0    -6 

0.0 

0.0 

-3    -7 

0.9 

8.9 

-6    -S 

+    12.7 

1.2 

.8 

-8 

+      3.6            0.0 

1    -6 

+      M 

+    W 

-2    -7 

+      0.5 

1.1 

Retained  Term*  of  the  Force*. 

X, 

T. 

Zi 

Xi 

T, 

Zi 

cos 

sin 

cos 

sin 

COB 

sin 

cos 

sin 

cos 

sin 

cos 

sin 

0    0 

1*73.1 

0.0 

+    66.7 

0.0 

-  550.6 

0.0 

3  -2 

+  441.0 

-  143.0 

-    64.6 

+  280.1 

+  356.7 

+  329.5 

1     0 

+ 

:i7n7>  -  224.0 

-  180.6 

+  3507.2 

+1456.4 

+1647.6 

4  -2 

+  149.4 

- 

0.2 

-    20.1 

+    51.7 

.   eu 

+    85.8 

2     0 

+ 

271.4  + 

29.2 

-    (il.n 

+    290.6 

+    40.6 

•       !!."..  4 

5  -2 

+    23.8 

- 

9.4 

+     11.4 

+    46.9 

+     2J.!t 

+    23.3 

3     0 

• 

:..-,.  i 

36.5 

+    43.1 

+      22.9 

+    33.4 

+      6.7 

6  -2 

+    15.9 

- 

12.6 

16.2 

-     13.1 

4     0 

• 

11.  (i  - 

7.4 

+       7.5 

+      49.4 

+      7.8 

+      7.2 

7  -2 

- 

1.5 

+ 

7.7 

+    24.8 

+     11 

.7 

5     0 

• 

1.2 

- 

3.8 

13.1 

31.6 

8  -2 

1.2 

- 

3.9 

15.0 

0.1 

6     0 

• 

1.8 

0.0 

+    27.5 

+      27.0 

7     0 

1.1 

_ 

1.1 

•    34.1 

14.4 

-3  -3 

- 

'.0 

+ 

2.2 

+ 

4.8 

-      8.8 

-     ,, 

• 

1.0 

0.0 

+     19.0 

0.0 

-2  -3 

+      0.3 

_ 

1.2 

- 

4.2 

+      6.7 

-1  -3 

- 

18.7 

- 

6.4 

- 

3.9 

+    10.7 

-5  -1 

- 

17.4  + 

4.8 

3.7 

+        1.3 

0  -3 

+  174.3 

+ 

60.3 

+    50.5 

-  170.8 

+    60.7 

-    32.6 

-4  -1 

1.9 

+      7.6 

3.4 

1  -3 

-1941.3 

+  366.8 

+  416.3 

+1909.7 

-  252.3 

+  367.8 

-3  - 

• 

•Jl.l    • 

4.8 

+      2.7 

+        0.2 

2  -3 

+5242.4 

-  845.2 

-  9f,«.4 

-5136.7 

+  641.7 

-  9:Ci.l 

-2  - 

• 

i,.  > 

. 

79.6 

+    72.3 

-      30.3 

+    33.6 

+      6.8 

3  -3 

+  715.6 

- 

40.8 

-    93.8 

-  902.6 

-  120.1 

-  238.2 

-1  - 

298.8 

- 

56.1 

-      5.9 

+    290.8 

-  156.4 

+  148.1 

4  -3 

+  264.1 

- 

91.3 

46.1 

-    51 

.•J 

+  165.7 

+  109.8 

0  - 

• 

•J.VJ1.:, 

- 

9.2 

-  274.4 

-  2319.6 

+  946.0 

-1066.3 

5  -3 

+ 

87.3 

- 

26.9 

-    21.3 

+    18.1 

+    55.0 

+    49.7 

1  - 

l.:i".- 

-    ll-.-J 

+  146.4 

+    239.5 

-712.7 

-  136.9 

6  -3 

• 

17.8 

- 

4.8 

+ 

1.9 

+      2.3 

+    19.4 

+     1X1 

2  - 

• 

1100.5 

-  208.3 

-    83^ 

+  1111.2 

+  742.9 

+  793.3 

7  -3 

1 

6^8 

- 

8.8 

- 

4.0 

+      7.0 

3  - 

• 

170.0 

- 

14.4 

-    22.2 

+    189.0 

+    93.1 

+  126.7 

8  -3 

- 

4.9 

1 

4.3 

- 

l.i. 

-      5.4 

• 

4  - 

• 

60.0 

- 

18.5 

+       4.5 

+      46.9 

+    30.0 

+    21.6 

1    5  - 

. 

7.9 

- 

0.8 

+     11.4 

+        5.3 

-2  -4 

• 

13.6- 

8.6 

- 

0.4 

+       1.3 

+     18.5 

+      1.5 

6  - 

• 

15.4 

_ 

11.4 

4-1 

+        7.7 

-1  -4 

- 

9.4  + 

16.2 

+ 

2.6 

-      3.2 

•     15.4  +      0.5 

7  - 
8  - 

• 
• 

6.9 
2.2 

t 

8.3 
6.5 

+      145 
+      5-4 

6.8 
+        2.1 

0  -4 
1  -4 
2  -4 

•    48.1  -    24.1 

+  327.4  1+      6.0 
-1374.1  +  339.5 

-    10.2+    48.4 
14.5  -  315.9 
+  377.7+1337.6 

-      9.5  +      5.2 
+    WJI-    58.1 

1  :,.-,.  1  +  274.1 

-4  -2 

13.7 

- 

1.2 

0.4 

+       25.9 

3  -4 

+2445.8  -  526.!» 

-  576.6 

-2365.7 

+  290.1  -  439.8 

-3  -2 

• 

11.1 

- 

2.4 

-      7.6 

24.2 

4  -4 

+ 

567.4  - 

-1.7 

-  116.2 

-  665 

:: 

•    48.3 

-  162.0 

-2  -2 

-• 

4.1 

• 

9.2 

+    22.3 

+       12.4 

5  -4 

• 

•Jii4.ii  -    65.5 

-    43.2 

-  113.2 

+     75.9 

+    24.5 

-i  -a 

• 

1211.-)  +  109.7 

+    86.1 

•     135.!! 

+    63.1 

i  .-..:? 

6  -4 

t 

39.5  - 

14.6 

13.4 

•     21 

1 

+    31.9 

+    22.7 

o  -a 

- 

3339.0  +  294.1 

+  393^ 

+  3296.3 

-  428.2 

+  589.8 

7  -* 

1 

31.2- 

17.1 

- 

8.3 

+      1 

•' 

1  -2 

+10242.4  -1049.0 

-1302.1 

-10042.0 

-1317.9 

-1799.0 

8  -4 

- 

13.2  + 

6-9 

- 

•J.7 

16.7 

2  -2 

337.0  + 

61.6 

+    21.0 

-    P20.1 

:;  >::.• 

-  271.8 

Retained  Terms  of  the  Forces. 

Xi 

Yi 

Z. 

X, 

Yi 

Zi 

i,    i' 

cos 

sin 

cos 

sin 

CO9 

sin 

cos 

sin 

cos 

sin 

cos 

sin 

-1  -5 

-      2.3 

+      4.6 

-      5.3 

+      0.9 

+    33.3 

+      2.5 

9  -6 

-    21.0 

+      3.9 

-      3.9 

-    20.8 

0  -5 

+      2.5 

-      2.0 

+      8.7 

1.4 

14.4 

-      0.2 

1  -5 

-    46.7 

-      0.6 

-    11.0 

+     44.7 

-      8.7 

4       7.8 

1   -7 

-      6.0 

•    13.2 

+      4.5 

+      6.9 

+    32.3 

1.5 

2  -5 

+  261.0 

•    44.9 

-    43.0 

-  252.9 

+    44.5 

-    52.1 

2  -7 

+    21.2 

+     10.3 

4.7 

•     12.5 

-      2.5 

1.0 

3  -5 

-  804.6 

+  266.5 

+  276.2 

+  790.9 

-    81.9 

+  168.1 

3  -7 

-    53.6 

+      1.2 

+     12.9 

+    42.8 

5.0 

+      8.0 

4  -5 

+1037.1 

-  288.1 

-  306.7 

-1000.8 

+  122.8 

-  191.4 

4  -7 

+  133.3 

-    42.0 

-    51.5 

-  120.4 

+     13.2 

-    27.0 

5  -5 

+  385.4 

-    77.0 

-    96.6 

-  407.2 

•     18.8 

-    95.6 

5  -7 

-  223.6 

+  106.2 

+  113.6 

+  229.7 

-    15.5 

+    50.5 

6  -5 

+  119.0 

-    37.1 

-    38.9 

-    98.4 

+    31.6 

2.1 

6  -7 

+  149.6 

-    58.5 

-    79.5 

-  171.2 

+     17.1 

-    30.6 

7  -5 

+     40.8 

-    29.4 

-      3.0 

-     37.0 

+     18.4 

+      5.6 

7  -7 

+  148.6 

-    45.4 

-    39.2 

-    83.3 

-      0.5 

-    20.7 

8  -5 

-    16.9 

+      9.9 

-    19.2 

-    29.0 

8  -7 

+    23.1 

-      7.7 

6.3 

-    45.1 

9  -5 

-    12.4 

+      3.4 

-      3.3 

12.3 

9  -7 

-      9.7 

+    12.0 

-     11.9 

-      9.7 

-2  -6 

-    11.2 

+      6.2 

-  ,  19.4 

-     19.9 

-1  -8 

+      5.2 

-    17.5 

•    17.5 

5.1 

-1  -6 

+      1.7 

-      7.3 

+    24.2 

+     11.4 

-    30.3 

-      2.1 

0  -8 

+      2,8 

+     19.0 

+    18.9 

1.2 

+    24.0 

+      1.6 

0  -6 

+      0.3 

+      9.0 

-    26.7 

+       0.5 

+    25.7 

+      1.6 

1  -8 

-    12.6 

-    16.4 

-    16.2 

+      9.1 

-    37.9 

+      l.fl 

1  -6 

+      0.4 

6.0 

+    25.9 

16.4 

-      8.3 

2.4 

2  -8 

+    13.1 

+    12.6 

+     12.4 

-    12.1 

+     16.8 

2.3 

2  -6 

-    37.7 

+     10.0 

15.1 

+     64.1 

-      9.8 

+     11.9 

3  -8 

-      8.7 

-      7.3 

6.3 

+      9.4 

1.9 

+    '0.8 

3  -6 

+  175.4 

-    55.6 

-    44.8 

-  205.8 

+    25.6 

-    43.0 

4  -8 

9.8 

+      9.3 

+      9.4 

+    10.2 

-      0.7 

+      3.1 

4  -6 

-  424.6 

+  177.8 

+  181.2 

+  459.3 

-    38.5 

+    98.1 

5  -8 

+    62.0 

-    26.9 

-     28.9 

-    66.9 

+      5.6 

•    13.7 

5  -6 

+  411.7 

-  136.9 

-  159.7 

-  422.5 

+    49.2 

-    80.5 

6  -8 

-    93.5 

+    50.5 

+     58.8 

+  104.6 

3.6 

+    21.0 

6  -6 

+  228.2 

-    55.2 

•    50.9 

-  192.7 

-      5.7 

-    47.5 

7  -8 

+    42.2 

4.2 

•    16.6 

-    72.7 

+      5.3 

9.6 

7  -6 

+    89.2 

-    22.3 

•    54.2 

•     93.4 

+     10.5 

-      8.1 

8  -8 

+    24.9 

-    38.7 

-    19.7 

-    10.6 

8  -6 

-    22.5 

-      8.9 

+      0.8 

•    50.31 

For  the  computation  of 


and 


yro  


dt 


we  have  the  above  series  for  xt  and  yt  with  reversed  signs,  and 


^!  =  +0.00003  +  4.02388  cos  M 

+  0.86552  cos  2  M 
+  0.20922  cos  3  M 
+  0.05330  cos  4  M 
+  0.01 392  cos  5  M 
+  0.00380  cos  6  M 
+  0.00112  cos  7  M 
+  0.00028  cos  8  M 

These  multiplications  furnish  us  now  finally  the  material  for  the  formation  of  the  differential  equation  for 
r°  8  r,  namely,  of 


=  —4.07365  sin  M 
—0.87270  sin  2  M 
—0.21058  sin  3  M 
—0.05352  sin  4  M 
—0.01402  sinSJUf 
—0.00375  sin  6  M 
— 0.00 100  sin  7  M 


•  +  ! 


•m) 


—r°R°-\-  2fc° 


Ternu  of  2  retained  fur  integration. 

i,     f 

CO* 

tin 

«,     »' 

cot 

>in 

i,      •' 

co» 

•in 

i.     i' 

cot 

tin 

0       n 

+  9109.8 

0.0 

-1    -2 

-.'11.7 

nu 

4    -4 

+8063.0 

I-.-.H.M 

6    -6 

rhn:i.r, 

-350.0 

1       0 

-  7en.it 

+  561.  (i 

0    -2 

4-  311:1.1; 

+  435.3 

5    -4 

+3015.7 

MSJ 

7    -« 

+  677.6 

Mfcl 

a     o 

I3J 

-  877.8 

1    -2 

BMU 

-.i-.".; 

6    -4 

+  950.1 

-  251.7 

8    -€ 

.  aau 

-129.7 

3       0 

:u  .4 

1  I-J.-J 

9    -2 

•M-.'.-,I..-. 

-6036.5 

7    -4 

•   i:i:,.i; 

-    60.2 

4       0 

•        '-T-li 

3    -2 

+  8109.5 

-  413.2 

1    -7 

+    28.7 

+  535 

:,      n 

-      35.0 

I-.'J 

4    -2 

•    I.M-.I 

ITU 

1    -5 

+    77.2 

in.'! 

9    -7 

+  157.4 

-  70.3 

6       0 

•       30.0 

U 

6    -2 

i-    431.0 

-    90.6 

2    -5 

i,  :!-..' 

•    16.8 

3    -7 

+  130.5 

+    2.7 

7       0 

-      29.5 

+  ai.7 

3    -5 

+1875.3 

-  439.1 

4    -7 

-  307.2 

+  62.4 

8       0 

+       14.1 

n.'. 

0    -3 

-    206.1 

1  !!>.!> 

4    -5 

-3827.3 

•1  .'-".  1 

5    -7 

+  609.7 

-243.4 

9      0 

+        3.0 

•    •-">.'. 

1     -3 

.  :.(,  !•>.:. 

+    26.7 

5    -5 

+2916.8 

-  851.0 

6    -7 

-  783.2 

.:'.--.- 

2    -3 

-15678.7 

+3104.7 

6    -5 

+1588.1 

-  379.9 

7    -7 

+  289.9 

-139.6 

•J       1 

+      10.1 

-    80.2 

3    -3 

1-90)61.9 

:n,u-,.i 

7    -5 

+  501.0 

-  127.7 

8    -7 

+  365.4 

-123.3 

-1     - 

+  686.0 

4    -3 

.  M.M.I 

i.  .'-..i 

8    -5 

+  192.7 

-    75.1 

0    - 

11.5 

5    -3 

.    l:\in.,, 

-  321.7 

2    -8 

+  101.2 

+120.2 

1     - 

-1084.2 

6    -3 

+     330.1 

-  126.3 

0    -6 

-    29.7 

-    74.4 

3    -8 

+  105.6 

+  96.9 

a  - 

HM4 

-t-  760.8 

1     -« 

+    92.7 

+  123.8 

4    -S 

-    28.5 

-  313 

3    - 

-    361.1 

HU 

0    -4 

+       67.5 

+    56.3 

9    -6 

+  370.1 

+  256.6 

5    -8 

-    85.7 

+  51.5 

4     - 

99.9 

-  116.9 

1    -4 

+    399.3 

+    32.9 

3    -6 

-  440.1 

+    30.6 

6    -8 

+  272.2 

-123.8 

5    - 

+      34.7 

IV  1 

2    -4 

•   :;-."  1.'' 

-  388.5 

4    -6 

+1089.6 

-  344.7 

7    -8 

-  311.7 

4  15M.il 

3    -4 

:•>'  ;:,.i 

'•iOTl.li 

5    -6 

-1794.8 

+  723.2 

8    -8 

•   ii:i.:' 

-   iT.r, 

For  ilie  computation  of  the  coefficients  of  integration  we  have,  — 

3.008587  logp,  9.87395» 

7.248165  "  Pl  0.35322 


log/i 
.      365.25 

g  208266 


log  /i'  2.4758o8 
"  /i  +  0.256752 
"  p!  +  9.724023 

M       1.806142 

/i'      0.529691 

p  and  q  are  the  coefficients  in  the  series  for  x,  and  yt. 


«  pt  9.38308 
«  pt  8.58950 
«  p4  7.86982 
«  p,  7.19033 
«  p,  6.54407 


log  q,  0.34788 

«  y,  9.37951 

«  9,  8.58670 

"  q,  7.86747 

"  &  7.19033 

"  y,  6.54407 


9.288603 


log         9.743248 


1.806142 


0.529691 


2p  3.612284 

2/i'  1.059382 

3,.  5.418426 

8/1'  1.589073 

4  p  7.224568 

4M'  2.118764 

5  M  9.030710 

5/i'  2.648455 

«/•  10.836852 

6/  3.178146 

7M  12.642996 

7  /i'  3.707837 

8/>  14.449136 

8/  4.237528 

9M  16.255278 

9M'  4.767219 

10/i  18.061420 

ll/i  19.867562 

10 


Log  of  the  "  Entwickelungs-Factoren." 


t      H 

i  -I-  4  and  i  —  4  < 

(  4- 


0 


+3,       +1  +4, 

68480»    7.33105 


+5, 
-H, 


-1 
—  5 


i  -f-  3  and  t  —  3 


+2,        +1 

6.02698w 


4-3,          0 
0,        —3 

7.92534 


+4,       -1  +5,       -2    . 

7J90573»     6.40380* 


+2,  0  +3,       -1  +4,       -2  +«,       -3    .  , 

0,       —2  +1,       —3  +2,       -4  -1-3,       —5    ., 

8.54206   8.52827n  7.01565»  5.66881n 


t'+landt  — 1 


+1,          0  -f  2,        -1  +3,       -2  +4,       -3    .  , 

0,       —1  +1,       -2  +2,       -3  +3,        — *    .  . 

9.20940       9.19653w     7.65594»     6.28942n 


+1,       -1  +2,        —2  +3,       -3  +4,        —1    .  , 

9.98970«     8.35223w     6.94297»     5.62793n 


The  numbers  above  the  logarithms  are  those  which  constitute  ±  x  in  i 


Specimen  of  the  Tables  of  Divisors. 

For  the  Class  i'  =  0. 

—  ( 

_, 

—2 

-1 

0 

+1 

+2 

+3 

+4 

•H 

+8 

+7 

+8 

+9 

9.141  19n 

9-26613,, 

9-44221n 

9-74325,, 

00 

9-74325 

9-44221 

9-26613 

9-14119 

9-04428 

8-96510 

8-89815 

8-84016 

8-78900 

-5 

9-04428,, 

8.18547 

8-31041 

8-48649 

8-78753 

8-08856,, 

8-78753,, 

8-48649n 

S.  31011,, 

-4 

9-14119,, 

8.40732 

8-58340 

8-88444 

8-28238,, 

8-88444, 

8  -68340,, 

8.40732,, 

8-28238, 

-3 

9-26613,, 

8-70834 

9-00938 

S-53226n 

9-00938B 

8-70S34n 

8.53226,, 

8-40732, 

8-31041, 

-2 

9-44221,, 

9-18546 

8-88442,, 

9-18566,, 

8-88442,, 

8-  70834, 

8-56340, 

8-48649, 

8-40731, 

-1 

9-74325, 

9-48650n 

9-48650n 

9-18546n 

9-0093R, 

8-88444, 

8-78753, 

8-70835,, 

8-64140, 

0 

00 

9-48650n 

8-8844  2n 

8-53226, 

8-28238, 

8-08856, 

7-93020,, 

7-79630, 

7-68032,, 

+1 

9-74325 

9-18546 

9-00938 

8-88444 

8-78753 

8-70835 

8-64140 

8-58341 

8-53225 

+2 

9-44251 

8-70834 

8-58340 

8-48649 

8-40731 

8-34036 

8-28237 

8-23121 

+3 

9-26613 

8-40732 

8-31041 

8-23123 

8-16428 

•8-10629 

8-05513 

+4 

9-14119 

8-18547 

8-10629 

8-03934 

7.98125 

7-93019 

+5 

9-04428 

8-00938 

7-94243 

7-88444 

7-83328 

+6 

8-96510 

7-86325 

7-80526 

7-75410 

+7 

8-89815 

7-73831 

7-68715 

+8 

8-84016 

7-62916 

When  for  this  class  t'  =  0,  one  of  the  divisors  in  j-. ^ — —T-. ^— ,  becomes  zero  we  have  to  put  down 

the  negative  square  of  that  divisor  which  retains  a  real  value.  This  table  of  the  divisor  for  i'  =  0  and  for  the 
coefficients  of  integration  ff  (i  -\-  x)  is  changed  into  the  table  of  the  divisors  for  f\  (i  -\-  x)  by  squaring  all  the 
numbers  and  by  adding  to  the  logarithms  of  the  squares  log  (c  -(-  c1)  fi.  Excepted  herefrom  are  the  terms  for 
which  c  or  c'  becomes  zero.  Those  terms  are  to  be  multiplied  by  —  or  — . 


11 


S/H-riiifn  "f'  tin'   '/'//</'.<  »/'  lln    ('•••                  •<  Integration. 

i'  =  0. 

/-« 

/-• 

/-» 

/-I 

/o 

/+! 

/+* 

'    '     • 

/+« 

/+• 

/+« 

/+T 

2 

_ 

-   ,  ,.,«-..<•. 

u 

M 

+0-101  iaT 

+0400W 

,1 

+040008 

.  m 

i         »  •  '-   | 

.....  .  .  • 

...,.--  ]-• 

•  ,,.,  

i  ;    : 

....  .*.-  i 

...     .     . 

-  .•-!•, 

t,  .  .  . 

,.,,.• 

-....-  ..-  i 

.....  .-i  , 

-  ...,,. 

_ 

-040014 

+040011 

MM 

-040*71 

-......-:•,• 

-0400tl 

-04001B 

...  ..... 

_ 

+040008 

MU 

-0-00071 

-0-OOW1 

-0490M* 

-040010 

-040007 

-041  179 

- 

+0400IJ 

-04001J 

.  , 

-0-00030- 

-04  HW* 

-0-00011 

-041141 

_ 

-040004 

-040007 

-040011 

-040877* 

-040MO 

-7 

-„..„..  ,,' 

-  • 

In  surh  a  talili-  ii  i-  only  ii<'c-<-s-ary  to  n>iii|>nti-  the  values  on  one  side  of  the  diagonal  line  of  asterisks,  since 
tin-  values  ap|>oar  on  both  sides  arranged  in  the  same  manner  as  [o  6],  [a  c~],  [i  c],  with  respect  to  [o  a],  [64] 
in  iln-  method  of  least  squares.  By  means  of  the  horizontal  sums  ?  the  coefficients  are  checked  because  of 


v  f  /,'  _L  .   ^  —  _ 


n 


•  +  1,  o  c  - 


2  * 


. 

(•  +  2.  o  (•  -  2. 


89, 


. 

(• 


r'ir 

«,   ••' 

CO* 

lin 

i,      i' 

cos 

sin 

>,     ••' 

CO* 

•in 

i       i' 
•p 

CO* 

Mil 

0      0 

+  4I.67< 

0.0 

0    -2 

+  9933.9 

-  7.VI.7 

5    -4 

-  61.9 

+11.5 

-1     -7 

+     1.3 

-    3.6 

1     (1 

-I-.0.6M 

-3607..VJ' 

1    -2 

-12287.5 

+1166.2 

6    -4 

-  15.0 

+  3.9 

0    -7 

+    7.9 

-  21.8 

2    o 

-  i:u« 

-  397.60< 

2    -2 

-21290.5 

+2442.7 

7    -4 

-    1.8 

+  0.5 

1    -7 

+  64.1 

-210.9 

3      0 

-    2.6U 

-    64.08/ 

3    -2 

-  2306.4 

+  229.2 

2    -7 

-  31.3 

+  22.5 

4      0 

0.0 

-    12.83/ 

4    -2 

-    371.6 

+    50.1 

-1    -5 

+    2.2 

-  0.7 

3    -7 

+148-5 

+  87.3 

.-,     tl 

0.0 

-      2.5K 

5    -2 

-      46.1 

+      6.0 

0    -5 

+  14.2 

-  4.0 

4    -7 

+  51  .3 

+    :u 

1    -5 

+127.2 

-  9.3 

5    -7 

-  19.2 

+  10.6 

0       0 

+  2936.7 

0.0 

-3    -3 

1.0 

-      0.6 

2    -5 

-138.4 

-29.3 

6    -7 

+  17.3 

•    8.0 

1       0 

-    !*£>.2 

+      19.8 

-2    -3 

-      44.5 

-      3.4 

3    -5 

-433.7 

+80.6 

7    -7 

-    3.7 

•    1.9 

2      0 

-    210.4 

+     105.3 

-1     -3 

-    276.0 

-    23.1 

4    -5 

+184.0 

-67.4 

8    -7 

-    3.3 

+    1.1 

3      0 

-      25.8 

+      11.-.' 

0    -3 

-  2694.8 

-  192.4 

5    -5 

-  77.9 

+21.7 

4       0 

6.2 

+        !.'-> 

1     -3 

-  3380.5 

•Ill-.l 

6    -5 

-25.7 

+  5.8 

0    -8 

+    1.7 

+    2.1 

2    -3 

+18286.1 

-3229.5 

7    -5 

-    M 

+  1.5 

1    -8 

+  13.0 

+  i:>.7 

-3    - 

-      15.5 

3.7 

3    -3 

-    155.7 

+    30.7 

8    -5 

-    1.4 

0.0 

2    -8 

+  14.3 

+  22.4 

-a  - 

-    111.9 

-       1  :..-.' 

4     -3 

+      17.1 

-    13.5 

3    -8 

+  32.1 

+  24.5 

-i   - 

-    969.8 

-   5»i:i.:t 

5    -3 

+        3.3 

-      0.4 

-1    -€ 

+    0.2 

+  1.2 

4    -8 

+  13.9 

+  :-'.- 

0     - 

-  4613.1 

+    388.3 

6    -3 

9.6 

+      2.4 

0    -6 

+    6.3 

+17.9 

5    -8 

+    5.6 

•    1.1 

i   - 

+10401.0 

-    584.0 

1     -6 

-  27.4 

+15.8 

6    -9 

-    6.3 

+    3.1 

2    - 

+  2177.7 

-    221.7 

-2    -4 

+        1.5 

-      0.4 

2    -6 

+  28.2 

+51.6 

7    -8 

+    4-r> 

-    2.3 

3    - 

+     1M.> 

+        3.1 

-1    -4 

+        4.6 

-       2.3 

3    -6 

+279.0 

+42.3 

8    -8 

1.2 

0.0 

4    - 

+ 

0.4 

0    -4 

+      32.0 

-    33.7 

4    -6 

K.1 

+30.5 

1    -4 

-    716.1 

+    96.8 

5    -6 

+  59.2 

-21.5 

6    -9 

+     1.5 

-    0.9 

-3    -2 

+        8.3 

+        1.5 

2    -4 

+  2107.7 

-  14.-..9 

6    -6 

-  17.3 

+  6.0 

7     -9 

-    2.2 

+    1.0 

-2    -2 

+     1  i-.-.r. 

2.2 

3    -4 

+  1322.9 

-  •,'-... 

7    -€ 

-    7.9 

+  2.4 

8    -9 

+    0.4 

-    0.8 

-1    -2 

+    960.0 

+      17.4 

4     -4 

-    264.9 

+    66.3 

8    -6 

-    2.8 

+  1.0 

9    -9 

-    0.1 

0.0 

For  the   formation   of  the   differential   equations   for   J,  and    i^    it   is   necessary  to  multiply  r"  8  r  with 


12 


3^'  XL  —  4-  1.04488  4-  5.01118  cos  M  ~  . 

+  3.00 130  cos  2  M 
4-  1.38657  cosSJf 
4-  0.56905  cos4Jif 
+  0.2 1828  cos  5  M 
4-  0.08089  cos  6  M 
4-0.03161  cos7M 
4-  0.00979  cos  8  M 

Having  performed  these  multiplications  we  obtain  for  integration 


.    K 


4-  4.39501  sin  Jf 
4-  2.81725  sin  2  Af 
-f.  1.33137  sin  3  M 
+  0.55228  sin  4  Jf 
4- 0.21 259  sinSJSf 
4-0.07719  sin6J!f 
4-  0.02454  sin  7  J!f 


and  simply 


~df~* 

d*6   - 
df    i 


li. 


«,  '•' 

Jj 

*2 

t,    «"' 

** 

** 

cos 

sin 

cos 

sin 

COS 

sin 

cos 

sin 

0      0 

-    293.0* 

0.0 

-  8731.9* 

0.0 

4    -1 

+  9901.6 

-    687.9 

+    639.9 

+  9298.1 

1       0 

-     157.8* 

+    878.7* 

•-  6465.1* 

+      28.9* 

5    -1 

+  4485.2 

-    293.2 

+    293.5 

+  4324.0 

2      0 

-    300.4* 

-  7176.5* 

+  5387.1* 

-    241.4* 

6    -1 

+  1848.4 

•     128.2 

+     108.6 

+  1792.8 

3       0 

•     204.0* 

-  5548.1* 

+  4985.9* 

•     187.2* 

7    -1 

+    707.7 

-      35.2 

+      42.0 

+    685.0 

4      0 

-    103.3* 

-  2019.2* 

+  2747.8* 

-      98.1* 

5      0 

44.5* 

-  1300.9* 

+  1255.3* 

42.8* 

-5    -2 

+    642.1 

+      12.6 

+      10.6 

-    722.2 

6      0 

17.7* 

-    525.2* 

+    523.1* 

16-7* 

-4    -2 

+  1486.2 

+      29.1 

+      24.1 

-  1432.4 

7       0 

6.5* 

-    205.2* 

+    214.3* 

5.8* 

-3    -2 

+  2815.4 

+     1C6.1 

+     100.8 

-  2580.8 

8       0 

2.5* 

-      86.7* 

+      72.6* 

2.2* 

-2    -2 

+  2684.3 

+    452.4 

+    471.5 

-  1797.5 

9       0 

1.0* 

-      29.0* 

+        9.4* 

0-3* 

-1    -2 

-  7484.1 

+  1745.8 

+  1767.9 

+10518.1 

10       0 

0.1* 

3.9* 

+        1.6* 

0.0 

0    -2 

-54730.2 

+  6308.1 

+  6527.9 

+64290.9 

CHECK. 

CHECK. 

1    -2 

-33213.1 

+  4804.2 

+  6058.7 

+63561.3 

I  a'a  />„+!  Sa'apm=  +0.72b'mq^  +0.2 

=  +0.2           =-1.3 

2    -2 

-43437.6 

+  5071.7 

-    911-5 

-  7514.1 

3    -2 

-67573.3 

+  7582.9 

-  6459.1 

-56034.2 

0      0 

-  1018.5 

0.0 

+    266.3 

0.0 

4    -2 

-43662.0 

+  4902-5 

-  4521-2 

-40231.6 

1      0 

+15182.5 

-      28.1 

+    162.6 

+15375.4 

5    -2 

-21547.8 

+  2409.7 

-  2290-0 

-20489.0 

2      0 

+  5564.4 

+     173.9 

34.7 

+  5736.0 

6    -2 

-  9236.7 

+  1028.4 

-  1022.1 

-  8963.1 

3      0 

+  1767.9 

+    254.2 

-    196.5 

+  1794.1 

7    -2 

-  3643.3 

+    418.6 

-    375.7 

-  3553.1 

4       0 

+    493.1 

+     187.1 

172.2 

+    546.1 

8    -2 

-  1396.3 

+     152.9 

-    165.9 

-  1351.0 

5       0 

+     117.3 

+      92.0 

•     105.0 

+      88.9 

6       0 

+      27.6 

+      40.7 

12.6 

+      52.6 

-4    -3 

-    651.5 

85.0 

81.9 

+    655.5 

7       0 

+      12.2 

+      15.1 

-      50.0 

14.3 

-3    -3 

-  1374.1 

-    208.3 

-    196.8 

+  1267.2 

-2    -3 

-  1941.2 

•    493.8 

-    469.4 

+  1623.6 

-5    -1 

-    406.2 

85.9 

90.4 

+    427.5 

-1     -3 

+    389.6 

-  1075.9 

-    986.1 

-  1536.3 

-4    -1 

-    982.6 

-    212.8 

-     197.2  ' 

+    914.4 

0    -3 

+15466.8 

-  2231.2 

-  1968.7 

-19070.7 

-3    -1 

-  1719.4 

-    439.9 

-     409.9 

+  1568.1 

1    -3 

+32924.0 

-  7039.1 

-  6188.3 

-44406.5 

-2    -1 

-  1636.9 

-    655.5 

-    551.2 

+  1006.6 

2    -3 

+11266.3 

-  1666.8 

-  3073.1 

-16238.7 

-1    -1 

+  4032.3 

-    612.7 

-    215.2 

-  6026.3 

3    -3 

+39386.4 

-  6595.6 

+  5534.2 

+32608.6 

0    -1 

+24638.8 

-  2220.4 

-  1199.6 

-30750.9 

4    -3 

+24184.2 

-  4154.3 

+  374!).3 

+22344.9 

1    -1 

+  2392.2 

-    642.0 

633.8 

-16574.1 

5    -3 

+11285.6 

-  1951.6 

+  1832.9 

+10799.1 

2    -1 

+22618.3 

-  1611.4 

+    943.3 

+16076.1 

6    -3 

+  4654.2 

-    807.3 

+    782.0 

+  4512.8 

3    -1 

+18183.6 

-  1301.6 

+  1150.8 

+16159.8 

7    -3 

+  1770.4 

-    314.5 

+    294.3 

+  1739.2 

13 


1.    •' 

{,,, 

+J 

i,      «' 

s 

•j 

co« 

fin 

co* 

Mil 

cot 

cot 

tin 

-    a 

4     64X7 

•     10&8 

4     106.7 

4    636.1 

9    -6 

4    584.2 

+    270.1 

-1-      47.8 

-    556.3 

3    -6 

4    437.0 

+    203.4 

uu 

1265 

-2    -4 

+   nio.t; 

-     68.2 

-      56.7 

-    288.9 

4    -6 

+    358.0 

+    366.4 

-      36.9 

+    995.9 

l        I 

4    810.7 

101.6 

-     103.4 

-     7 

5    -6 

4    709.5 

+      42.1 

-    309.6 

-      87.7 

c       l 

•,-Jl.l 

-     l< 

-  2134.8 

6    -€ 

+    450.4 

3.1 

84.7 

+      71.9 

l        l 

4  6730.5 

-    7-."." 

-  <;i...  . 

-  6538.2 

7    -6 

+     162.7 

+        6.0 

-      73.3 

+       0.4 

a  -4 

4  1!).V..I 

-     «l-..7 

-    317.0 

-  2674.6 

4  7290.6 

-    885.8' 

-    204.7 

+  1960.0 

-2    -7 

4      645 

-    161.6 

-    161.9 

67.0 

4    -4 

•   . 

-    860.7 

+    698.4 

4  4901.3 

-1    -7 

+     l  .1.1, 

-    346.6 

•    304.2 

128.3 

I 

4  »;-!.•• 

-     3HG.5 

+     300.1 

+  2412.3 

'   0    -7 

-1-    239.2 

-     450.1 

367.1 

-    210.4 

6    -4 

+    906.7 

llll.l 

+      '.i-'.n 

4    861.4 

1    -7 

4    '-'- 

•    101.8 

+    234.0 

144.11 

7        1 

4    293.8 

-      37.9 

4      14.6 

+    267.7 

2    -7 

+    602.1 

-    301.2 

+  e>2.7 

•Jl'>.- 

3    -7 

4    23.'..-. 

165.7 

+    292.0 

-      25.8 

-1    -5 

•4      23.6 

-      Zt.!> 

-      30.9 

-      13.7 

4    -7 

4    533.2 

+      74.6 

117.3 

+    228.1 

0    -5 

-    1*1.0 

-      : 

-      13.9 

4    166.0 

5    -7 

+    140.3 

+    187.4 

+        9.8 

+    518^ 

1     -5 

-    770.1 

-      13.7 

+       9.7 

+    - 

6    -7 

+    283.7 

+       4.4 

•    151.0 

31.0 

-    414.6 

4       1  •„'.:. 

+      81.9 

4    801.6 

7    -7 

4    228.1 

-      28.0 

-      54.4 

+        9.6 

-  in: 

4     128.4 

+    243.3 

+     400.4 

4    -5 

-    210.8 

-     !!:!.'• 

-    378.3 

-  l  -  I--  1 

-1    -8 

4      49.6 

+      35.3 

+      32.3 

-      47.1 

-      18.1 

-    108.7 

-      24.7 

-    603.6 

0    -8 

+      85.2 

+    114.7 

+    104.7 

755 

6    -5 

-     169.1 

-      1 

-      32.8 

-     3(W5 

1    -8 

+      99.9 

+     107.1 

+      71.3 

74.1 

-     1.V..7 

8.3 

-      20.1 

-    207.0 

2    -8 

4    166.9 

+     158.9 

+      46.6 

73.9 

8    -5 

-    124.0 

+      95£ 

-      33.9 

-    128.7 

3    -8 

4    121.3 

+    131.4 

50.9 

+      24.9 

4    -8 

4    123.3 

+    129.5 

-      865 

+     104.0 

-1     -6 

4      71.7 

4    112.7 

r        134.3 

-      55.7 

5    -8 

4     154.8 

+      65.2 

107.3 

+      30.4 

0    -6 

4    164.4 

4     1- 

+    112.6 

-    154.6 

6    -8 

-      27.9 

+      89.5 

+      13.8 

+    155.1 

1    -€ 

4    453.6 

4    265.6 

+     173.0 

-    434.8 

7    -8 

+      57.3    '    +      18.4 

40.2 

-       55.8 

The  integration  of  the  preceding  three  differential  equations  gives  finally  the  perturbations  of  the  rectangu- 
lar co-ordinates. 


•',    •' 

| 

Ti 

ti 

cos 

tin 

cot 

sin 

cot 

sin 

0      0 

-    84.94* 

0.0 

-1022^1* 

0.0 

4  148J6TJ 

1       0 

-      4.74* 

44279.97* 

-4154.40* 

-    11.92* 

HH.« 

2      0 

4    25.65* 

41241.89* 

-1226.46* 

4    24.06* 

-    48.01* 

3      0 

4      8.30* 

4  325.86* 

-  322.92* 

4       8.27* 

-      7.72) 

4      0 

4      2.50* 

4    86.21* 

-    85.92* 

4      2.37* 

1.4lf< 

5      0 

4       0.68* 

4    22.96* 

-    22.70* 

0.0 

-      0.3K 

6      0 

4       0.16* 

4      6.19* 

-      6.02* 

0.0 

-      0.07* 

4      0.08* 

7      0 

0.0 

4      1.31* 

-      1.37* 

0.0 

0.0 

0.0 

0      0 

-  699.7 

0.0 

4    755 

0.0 

1       0 

411185 

-      6.6 

9.4 

4  901.6 

0.0 

2      0 

4  463-6 

-    31.7 

4    28.9 

4  433.4 

4  143.4 

:t     0 

4  100.7 

1.1.4 

4     13.1 

4    97.4 

4    42.2 

4      0 

4    23.3 

-      5.2 

4      4.9 

4    21.1 

4      gJi 

5      0 

4      6.8 

-      15 

4      1.7 

4      6.1 

4       1.0 

6      0 

4       0.8 

0.4 

4       0.1 

4      05 

4      048 

4       i'.-' 

-5    -I 

4       4.1 

4        1.1 

4        1.0 

-      4.0 

0.0 

-4    -\ 

4    32.1 

4      3.7 

4       35 

32-4 

4      0.8 

-      0.9 

i '' 


14 


I 

% 

Si 

*)       l 

COS 

sin 

cos 

sin 

COS 

sin 

-3    -1 

+     122.3 

+      11.8 

+      11.8 

-    122.9 

+        4.2 

4.5 

-2    -1 

+    494.5 

+      26.8 

+      26.3 

-    491.7 

+       2-J.7 

26.9 

-1    -1 

+  2208.5 

-      55.3 

72.4 

-  2188.4 

+    226.2 

-    236.6 

0    -1 

+  7732.7 

-    671.7 

-    325.3 

-  7809.7 

+    428.1 

318.4 

1     -1 

-  1340.7 

-      82.3 

0.9 

-  1289.8 

-     554.G 

+    231.4 

2    -1 

-  3739.2 

+    227.2 

-    192.7 

-  3658.9 

-    202.1 

114.3 

3    -1 

-  1092.5 

+      72.3 

70.3 

-  1081.8 

-      22.9 

10.7 

4    -1 

-    300.6 

+      19.9 

19.6 

-    300.2 

4.2 

1.6 

5    -1 

_      79.0 

+        5.0 

5.4 

84.8 

0.6 

0.3 

6    -1 

21.9 

+        1.3 

1.1 

-      20.7 

7    -1 

6.3 

0.0 

0.0 

6.1 

-5    -2 

6.6 

0.2 

0.2 

+        7.2 

-4    -2 

-      50.0 

+        1.9 

+        2.0 

+      52.5 

-3    -2 

-    192.0 

+        7.5 

+        7.8 

+    192.5 

1.7 

+        2.1 

-2    -2 

-    778.1 

+      36.1 

+      36.1 

+    779.4 

9.2 

+      12.0 

-1    -2 

-  3513.0 

+    213.1 

+    218.7 

+  3500.3 

-      72.0 

+       85.4 

0    -2 

-19149.5 

+  2127.3 

+  2083.7 

+19003.2 

-    428.6 

+    600.3 

1    -2 

-  8330.7 

+  1305.0 

+    754.2 

+  9254.2 

+    525.7 

-    767.6 

2    -2 

+10930.4 

-  1159.0 

+  1065.5 

+10367.5 

+    244.1 

146.5 

3    -2 

+  4932.9 

-    540.5 

+    540.7 

+  4849.2 

+        3.7 

46.1 

4    -2 

+  1507.9 

-    166.7 

+    166.1 

+  1497.3 

+        1.5 

7.4 

5    -2 

+    428.2 

-      47.6 

+      47.9 

+    432.3 

+        0.3 

1.4 

6    -2 

+    122.5 

-      13.7 

+      12.7 

+    112.6 

7    -2 

+      30.7 

3.5 

+        3.0 

+      29.9 

8    -2 

+        8.0 

0.8 

+        0.9 

+        7.7 

-4    -3 

1.9 

+        3.0 

+        2.8 

+        4.8 

-3    -3 

+      65.9 

+        3.6 

+        3.5 

-      66.1 

+        0.6 

0.7 

-2    -3 

+    245.3 

+      13.5 

+      13.2 

-    263.7 

+        3.3 

3.6 

-1    -3 

+  1128.7 

+      45.6 

+      42.7 

-  1120.9 

+      21.1 

22.1 

0    -3 

+  5724.9 

+        4.2 

15.3 

-  5630.2 

+     187.9 

-    208.4 

1    -3 

+  9598.9 

-  2097.8 

-  1894.6 

-  9736.8 

+     145.1 

-    246.1 

2    -3 

-  5031.4 

-      17.9      • 

+    509.0 

-  2272.5 

-    842.5 

+  1273.3 

3    -3 

-  3779.0 

+    539.8 

-    523.1 

-  3638.3 

-      69.4 

+    141.1 

4    -3 

-  1034.5 

+    161.6 

•     156.4 

-  1022.7 

18.6 

+      16.8 

5    -3 

-    268.1 

+      43.2 

-      42.6 

-    269.3 

-        3.7 

+        3.0 

6    -3 

80.4 

+      13.6 

9.6 

56.7 

0.7 

+        0.5 

7    -3 

17.7 

+        3.1 

3.0 

-      17.2 

8    -3 

4.0 

+        0.7 

0.6 

3.9 

-4    -4 

1.1 

+        1.1 

-3    -4       . 

+        1.4 

1.3 

-2    -4 

3.2 

+        1.4 

+        0.9 

+        2.7 

a 

0.3 

-1    -4 

0    -4 

8.9 
+        1.4 

+        1.2 
12.1 

+        1.2 
-      22.6 

+        9.3 

4.0 

+  i3 

+      27.9 

2.5 
-      21.9 

1    -4 

+  1826.7 

-    182.2 

•    135.1 

-  1854.9 

+       59.7 

-      91.2 

2    -4 

+    748.2 

120.8 

-    111.6 

-      32.3 

-     1&7 

+    217.7 

3    -4 

-    833.4 

+      99.3 

1.6 

-    402.4 

56.4 

+      80.2 

4     _4 

-    294.8 

+      40.7 

-      33.9 

-    250.5 

2.5 

+      14.8 

5    -4 

-      72.0 

+      10.1 

8.1 

66.4 

2.4 

+        0.9 

6    -4 

14.5 

+        1.8 

1.8 

16.4 

0.5 

7    -4 

3.4 

+        0.3 

2.9 

-2    -5 

1.6 

+        1.7 

15 


* 

ft 

f, 

',        *' 

tin 

CM 

tin 

CO* 

fin 

-1     -5 

10.1 

+           I.'' 

+        2.1 

•       10.4 

-       «.! 

+        M 

0    -5 

47.7 

+          '.'.' 

+        4.1 

+      46.9 

+    '•: 

+        1.3 

1     -5 

•J    -5 

•-•-.>•.'.  1 
-     148.9 

13.4 
+      21.4 

UfJ 

+        fr.VJ 

+    218.3 
+     188.6 

+   i:;.- 

+      104 

I'.l 

3    -r. 

+    204.2 

-      30.9 

40.0 

+        7.4 

+      80.9 

39.4 

4    -5 

+      20.8 

+        7.8 

+      20.2 

•     M:;.:I 

64 

+        84 

G    -5 

+        2.5 

+                ''   '  1 

+        1.1 

+      20.6 

•        04 

+        24 

6    -5 

+        3.1 

0.6 

+        04 

+        i..l 

04 

7    -5 

+        1.7 

+        2.4 

8    -5 

+        0.9 

+       0.9 

-2    -6 

+        0.7 

-        0.3 

+        0.2 

0.7 

-1    -6 

+        1.3 

24 

4.2 

1.9 

+        1.8 

0    -6 

+      14.0 

2.3 

-r          2.1 

14.4 

4.0 

$.3 

1     -6 

+     101.1 

•     141.0 

+     1264 

1874 

1.4 

2.7 

2    -4 

•f    1664 

+      64.2 

-      62.6 

-      66.6 

+        2.7 

84 

3    -6 

153.2 

-      : 

+      95.3 

-      77.5 

-      144 

+      22.4 

4    -6 

37.1 

-      324 

+      114 

-      87.9 

+        1.6 

54 

-6 

-      25.6 

3.1 

+      11.6 

14 

1.7 

+        2.6 

6    -6 

0.0 

0.3 

+        1.9 

2.2 

•        0.9 

7    -6 

-        23 

T                    0.0 

-3    -7 

04 

+        04 

0.2 

+        0.4 

-2    -7 

2.0 

+        4.3 

+        4.3 

+        2.1 

-1     -7 

9.4 

+      164 

+      15.9 

+        9.2 

1.0 

0    -7 

41.5 

+      57.1 

+      544 

+      41.9 

—     -5«3 

04 

1     -7 

-    237.0 

+    146.4 

+     103.9 

+    2344 

-     J3.3 

2    -7 

•     162.0 

-      86.7 

+    110.3 

-    238.0 

•      •*'.'< 

Jfft 

3    -7 

+    290.3 

153.9 

+     1374 

+    272.2 

8.9 

+       17.- 

4    -7 

-      20.6 

-      30.8 

+      37.4 

0.0 

2.5 

+       4.9 

5    -7 

2.3 

11.4 

+        4.1 

17.7 

+        0.3 

14 

6    -7 

5.4 

1.0 

+        4.1 

+        04 

0.4 

+        0.7 

7    -7 

2.4 

0.3 

+        1.3 

0.3 

-1     -8 

-       14 

1.4 

1.4 

+        1.7 

0    -8 

6.8 

8.3 

8.4 

+       6.1 

-     .  04 

1    -8 

-      16.8 

21.4 

-      22.0 

+      18.8 

+      15.5 

1.0 

2    -8 

+      46.1 

+      43.3 

+      30.6 

434 

+        1.4 

0.7 

3    -8 

-       44.0 

-       50.4 

46.7 

-      394 

4.0 

+       0.9 

4    -8 

-      12.4 

-       11.7 

-f       94 

14.1 

-        I'.  | 

0.4 

:.    -- 

7.7 

3.0 

+        5.4 

2.0 

-        04 

+       0.7 

6    -8 

•        04 

2.2 

0.1 

4.0 

04 

7    -8 

0.9 

+        0.3 

+       04 

+       04 

Normal  Placet  referred  to  the  Mean  Equinox  1854.0. 

Berlin  M.  T.                         „                             3                        Berlin  M.  T.                         a                             S 

1852,  July          1.0         271°  35  1643         -  8  35  16.00         1855,  April       26.0         223°  23  31.65         -  0  58  1&38 

1852,  October     1.0         274  56  46.02          -18  24  28.78         1856,  October  22.0           39  13  48.02          -  5  12  50.07 

1853,  January     1.0         322  28  46.75          -16    2  17.53         !«•>,  March     90.0         182    4  41.86          +  7  34     3.35 

1854,  January  28.0         128    3  16.18          +12    2  48.34         1859.  July          8.0         278    7  52.10          -  9  19    9.96 

16 


The  perturbations  computed  with  the  above  coefficients  for  the  times  of  the  normals  are  :  — 


Si 

+11421 
+  4084 
+  1750 
+39074 
+  2042 
+  1754 
+  5642 
+  8584 


-15176 

-19862 
-33592 

-  4084 

-  2185 
-14556 

-  2660 
-10494 


-2756 
-2823 
-2105 
+3665 
+  532 
-  380 
+2672 
-^500 


+14787 
+  9001 
+10510 
+38902 
+  2592 
+  5556 
+  6360 
+10653 


-10133 
-16524 

-30074 
+  6322 

-  1580 
-12885 

-  1575 

-  6160 


£ 

-  6858 

-  8192 
-11002 
+  1899 

-  98 

-  4268 
+  1788 

-  7252 


For  J, ,  »j, ,  f, ,  the  plane  of  the  orbit  of  Melpomene  is  the  fundamental  plane,  but  J,  rj,  J  are  referred  to  the 
equator.     The  transformation  is  effected  by  means  of  the  formulas  on  pages  391  and  392,     IB U"  /?5"7. 
We  derive  from  n'  =  16°  16'  53".3,     Q'  =  19°  16'  43".7,     and  »'  =  15°  28'  17".2  for  1854.0:  — 


cos  (*,  x)  =  +  0.959273 
cos  (y,*)  =  —  0.268411 
cos  (z,  at)  =  -f  0.088074 


cos  (a:,  y)  =  +  0.282146 
cos  (y,  y)  =  -f-  0.925742 
cos  (z,  y)  =  —  0.251799 


cos  (or,  z)  =  —  0.013949 
cos  (y,  z)  —  +  0.266394 
cos  (z,  z)  =  -|-  0.963765 


The  computation  of  the  normal  places  from  the  osculating  elements  for  1854.0  with  the  perturbations  J,  TJ,  £, 
gives  the  following  equations  of  condition  for  the  determination  of  the  corrections  of  the  elements  :  — 


+1.72507 

-3.46371 

+1.76341 

-0.01327 

+0.11791 

-  9.60585 

+  157.29' 

+1.05428 

-2.12179 

+0.96271 

-0.00356 

+0.03244 

-  5.53250 

+  26.24 

+0.98888 

-1.13494 

+0.69111 

-0.02955 

+0.01693 

-  3.91254 

-  184.68 

+1.54040 

+3.09070 

+1.69341 

-0.05026 

-0.05610 

+  0.38965 

-  508.67 

+1.05335 

-1.21848 

+1.51267 

-0.04736 

+0.35622 

+  5.19856 

+  75.05 

+3.21295 

+1.63979 

+2.06075 

-0.07675 

+0.47456 

+33.30130 

-1902.90 

+1.01318 

+0.73413 

+1.50797 

-0.08393 

+0.19514 

+15.62610 

-  219.44 

+1.85143 

-3.64800 

+1.80356 

-0.01777 

+0.07135 

+37.14650 

-  606.95 

dM 


S  <JP 


100 


-0.08528 

+0.22198 

-0.13034 

+0.17877 

+1.44227 

+  0.73639 

-    87.12 

-0.12241 

+0.18470 

-0.09555 

+0.17529 

+0.48963 

+  0.52905 

-    26.89 

+0.12166 

-0.18671 

+0.08963 

+0.12534 

-0.11444 

-  0.53821 

-    35.08 

-0.11837 

-0.24087 

-0.14720 

-0.27302 

-0.64995 

-  0.13495 

+    82.14 

-0.25846 

+0.20020 

-0.38766 

-0,08737 

+1.41267 

-  1.07558 

-    23.25 

+0.92431 

-0.01619 

+0.57207 

+0.16001 

-1.80113 

+  9.04078 

-  511.75 

-0.27122 

-0.25501 

-0.39779 

-0.21930 

+0.73969 

-  4.07944 

+    93.35 

-0.04169 

+0.15224 

-0.08194 

+0.20950 

+1.35572 

-  0.58380 

-    67.39. 

=  0 


From  which,  by  the  method  of  least  squares,  is  obtained  :  — 


=  -f-  12'  16".46 


8  <f  =  -\-  1'  33".89 
di  =  --0'  12".08 


9'0".57 
0".15125 


3  &  =  -f  2'  41".49 


and  thus  finally  the  pure  elliptical  elements  :  — 


o 

80 


Jf= 

n  =  15     5 

8  =  150     3  49.70 

*    =  10     9  16.85 

q,  =  12  34  20.18 

(i   =  1020".11977 

log  «  =  0.3609032 


1854,  Jan.  0,  Washington  Mean  Time. 

8  53.31 
5  30.95 


M.  Eq.  Ep. 


=16°  7  48"6 
=  19  16  5.9 
=  15  27  48.0 


With  these  element-,  ami  the  above  perturbations,  I  have  constructed  tables  which  represent  the  normal*  as 
follows :  — 

Jacoad  J3  J  a  cos  S  .13 

+L8  '-fa  —£2  +1.2 

—3.6  —4.3  +3.8  —0.8 

—2.0  —1.3  +5.5  —4.9 

—1.3  —2.3  —0.6  +1.4 

Tlii-  result  is  certainly  satisfactory,  since  the  perturbations  by  Suturn  have  been  neglected. 

For  curiosity's  sake  I  liave  computed  an  approximation  of  the  secular  variations  of  the  elements  from  iln- 
terms  multiplied  by  t.     They  are  :  — 


n    =+32".On 
Q  =  —  35.01  I  . 

i  =-  o^s/111 

9    =+    0.68  j 


II.    ON  THE  CONSTRUCTION  OF  THE  TABLES  OF  MELPOMENE. 


TDEFOEE  entering  into  the  details  of  the  construction  of  the  tables,  I  would  take  the  liberty  of  making  some 
general  remarks  on  the  treatment  of  asteroids  at  the  present  time. 

After  two  oppositions  it  is  possible  to  determine  the  elements  of  an  asteroid  near  enough  the  truth  for 
computing  the  perturbations,  and  I  think  those  by  Jupiter  are  sufficient  for  our  present  purposes.  Three 
oppositions,  then,  admit  the  more  accurate  determination  of  the  elements,  and  after  about  eight  oppositions 
they  can  be  finally  corrected  for  the  computation  of  the  general  perturbations  of  the  first  order  by  Jupiter. 
Preliminary  tables  constructed  upon  them  will  give,  for  the  next  fifty  years,  the  ephemeris  near  enough  to  find 
the  planet,  and  for  forming  normal  places.  After  that,  a  computer  can  do  something  definite  ;  then  he  may 
compute  the  perturbations  of  the  second  order  by  using  those  known  of  the  first  order,  or  he  may  find  it 
necessary  to  recompute  the  first  order  with  the  elements  upon  which  the  preliminary  tables  are  based.  And 
only  then  it  will  be  necessary  to  calculate  the  perturbations  by  Saturn  also.  Our  duty  in  our  time  with  re- 
spect to  the  asteroids  is,  to  avoid  all  superfluous  work  on  them,  and  to  get  out  as  soon  as  possible  such  prelim- 
inary tables.  Those  asteroids  which  are  of  special  interest,  as,  for  instance,  Leucothea  and  Euphrosyne  for  the 
determination  of  the  mass  of  Jupiter,  must  of  course  be  treated  in  a  different  manner.  For  those  it  will  be 
best  to  carry  on  the  special  perturbations  by  Saturn,  Jupiter,  Mars,  Earth,  and  Venus  for  a  number  of  years. 

A  number  of  small  terms  and  equations  have  been  omitted,  since  six  decimal  places  were  found  to  be  suffi- 
cient in  the  tables.  If  we  denote  the  Arguments  in  the  following  manner, 

I  =  -                   M'  XVI  =  —     M—  3M'  XXXI  =  5M—  ±M' 

11=          M-      M'  XVH=       iM—BM'  XXXII  =  3M—8M' 

111=          M—3M'  XVIII  =       5M—2M'  XXXIII  =  —  4  M-      M' 

IV  =          M—2M'  XIX  =       3M—7M'  XXXIV  =  7  M  —  2  M1 

V  =       2  M—  3M<  XX  =       5  M  —  3  M'  XXXV  =  5  M  —  6  M' 

VI  =       3M—2M'  XXI  =  —  2M—3M'  XXXVI  =  6M-      M' 

VII  =       2M-      M'  XXII  =          M—  7  M'  XXXVTI  =  ±M—5M< 

VHI  =  -      M—2M'  XXin=          M—5M'  XXXVIII  =  4M—7M' 

IX  =  -      M-      M1  XXIV  =       3M—5M'  XXXIX  =  M—8M' 

X  =          M—  4  M'  XXV  =  —  3  M—  2  M'  XL  =  7  M  —  3  M' 

XI  =          M  XXVI  =          M—GM'  XLI=:—     M—  5  M' 

XII  =       3M-      M'  XXVII  =       2M—7M'  XLII  =  -  M—1M' 

XIII  =       3  M—  4  M'  XXVIII  =       2  M—  5  M1  XLIII  =  -  M—±M> 

XIV  r=  —  2M-      M'  XXIX  =  —  3M-      M>  XLIV  —  5M—8M' 
XV  =       4M-      M'  XXX  =       5M—     M'  XLV  =  5M—7M' 

the  perturbations  are  :  — 


19 


i 

' 

k 

{ 

cot 

•in 

CO* 

(in 

CM 

•in* 

ii  M 

-I.'M' 

-1022.4  If 

+  14O67* 

M 

1.7  If 

+427" 

HV|.40f 

mm 

-  44«.23f 

+  493£Bf 

•J  M 

+     25-ti.V 

i.'ll.89f 

-1226.4« 

+    24.!Wf 

•     l-.ul/ 

+    53.1* 

:\M 

+     t.:M 

+  325.8« 

-  3*a.'.w 

+      8.27f 

-      7.72T 

+      8.561 

4.1A 

+      2.50* 

+    86.2U 

•    85.9* 

+      2UJ7f 

1.47< 

+      1^3f 

:.  M 

+     o.6«* 

+  aa/.iK/ 

•    22.7W 

0.3U 

i       0.34/ 

G.I/ 

+      0.1W 

+      O.i:«c 

!...'." 

-      OM7t 

+      0.08f 

7  .!/ 

+      1.31f 

1.37< 

I 

+  7732.7 

-    671.7 

-    325J 

-  7809.7 

+    428.1 

•    312.4 

I 

i  'ir.i.r. 

+  2127.3 

+  2083.7 

+19003.2 

MM 

+    600.3 

:t 

:  .•!.•• 

+        4.2 

15.3 

-  5630.2 

+    187.9 

208.4 

4 

+         1.4 

12.1 

•.••.M; 

4.0 

+      27.9 

21.9 

I 

47.7 

+       -.:> 

+        4.1 

+      46.9 

+        1.8 

+        1.3 

6 

+      14.0 

2.3 

•         2.1 

14.4 

4.0 

0.3 

7 

41.5 

+     r,7.i 

+      54.6 

+       41.9 

5.3 

0.5 

81 

&a 

8.3 

M 

+       6.1 

0.5 

II 

-  1340.7 

-.'.: 

(1.0 

-  1289.8 

-    654.6 

+     231.6 

•J  II 

•M 

-  1150.0 

+  1065.5 

+10367.5 

+    244.1 

MM 

311 

-  3779.0 

+    639.8 

-    :>•.':!.  i 

-  3638.3 

.,-.1 

+     141.1 

4  II 

-    !fiW.H 

+      4t>.7 

-      33.9 

-    250.5 

2-5 

+      14.8 

.1  II 

+        2.5 

+        2.9 

+        1.1 

+      20.6 

•         0.6 

+        £5 

611 

9.0 

ii.it 

+        1.9 

2.2 

+        0.9- 

7  II 

2.4 

0.3 

+        1.3 

0.3 

III 

+  !tt!>8.9 

-  2097^ 

-  1894.6 

T>.8 

+     145.1 

•    261.1 

2  III 

+     166^ 

•)•      64.2 

i,  -.'.(, 

-      66.6 

+       2.7 

2.5 

IV 

-  8330.7 

+  1305.0 

+    754.2 

+  9954.2 

+    525.7 

-    787.6 

2  IV 

+    748.2 

120.8 

lll.i. 

-      32.3 

131.7 

+    217.7 

31V 

1.  vi.;» 

78^ 

+     !>:>.:! 

-      77.5 

14.6 

+      22.4 

4  IV 

12.4 

11.7 

•       :M; 

-      14.1 

0.4 

0.4 

V 

-  5031.4 

-      17.9 

+    509.0 

-  2272^ 

•     -IV.:. 

+  1273.3 

av 

37.1 

-      32.5 

+      11^ 

-      87.9 

+       1.6 

5^ 

VI 

+  49:v.».!i 

-    540.5 

+    540.7 

+  4849.2 

+        3.7 

46.1 

a  vi 

144 

•f        1^ 

1.8 

16.4 

VII 

-  3739.2 

+•    227.2 

-    192.7 

-  3658.9 

-    202.1 

•     114.3 

2  VII 

+  1507.9 

166.7 

+    166.1 

+  1497.3 

+        1.5 

7A 

3  VII 

80.4 

-)•      13^ 

9.6 

-      56.7 

0.7 

+        03 

vin 

-  3513.0 

+    213.1 

+    218.7 

+  3500.3 

-      72.0 

+      85.4 

9  VIII 

3^ 

+        1.4 

-        0.9 

+       2.7 

IX 

+  2208.5 

:.:>.:! 

72.4 

-  218M 

+    226.2 

-    236.6 

•_'  IX 

77-.I 

+      36.1 

+      36.1 

+    779.4 

9.2 

+      12.0 

SIX 

+      65.9 

+        &6 

+        3-5 

66.1 

•            O.li 

0.7 

4  IX 

1.1 

+        1.1 

X 

+  1826.7 

182.2 

135.1 

-  1854.9 

+      69.7 

-      91.2 

ax 

+      46.1 

+      43.3 

+      39.6 

<u 

+        1.4 

0.7 

20 


• 

ft 

»a 

if, 

cos 

sin 

cos 

sin 

cos 

sin 

OXI 

-    699.7 

+      75.5 

-    202.6 

XI 

+  1118.5 

5.6 

9.4 

+    901.6 

+     129.9 

+    143.4 

2X1 

+    463.6 

31.7 

+      28.9 

+    433.4 

+      38.2 

+      42.2 

3X1 

+     100.7 

15.4 

+      13.1 

+      97.4 

+        5.2 

+        6.6 

4X1 

+      23.3 

5.2 

+        4.9 

+      21.1 

+        0.8 

+        1.0 

5X1 

+        5.8 

1.5 

+        1.7 

+        6.1 

XII 

-  1092.5 

+      72.3 

70.3 

-  1081.8 

22.9 

10.7 

2  XII 

+    122.5 

13.7 

+      12.7 

+    112.6 

xni 

-    833.4 

-t-      99.3 

1.6 

402.4 

56.4 

+      90.2 

2  XIII 

2.2 

4.0 

XIV 

+    494.5 

+      26.8 

+      26.3 

-    491.7 

+      22.7 

-      26.9 

2  XIV 

-      50.0 

+        1.9 

+        2.0 

+      52.5 

XV 

-    300.6 

+      19.9 

-      19.6 

-    300.2 

4.2 

1.6 

2  XV 

+        8.0 

0.8 

+        0.9 

+        7.7 

XVI 

+  1128.7 

+      45.6 

+      42.7 

-  1120.9 

+      21.1 

22.1 

XVII 

-  1034.5 

+     161.6 

-     156.4 

-  1022.7 

-      18.6 

+      16.8 

XVIII 

H    428.2 

47.6 

+      47.9 

+  '432.3 

1.4 

XIX 

f    290.3 

153.9 

+     137.5 

+    272.2 

8.9 

+      17.8 

XX 

-    268.1 

+      43.2 

42.6 

-    269.3 

3.7 

+        3.0 

XXI 

+    245.3 

+      13.5 

+      13.2 

-    263.7 

+        3.3 

3.6 

xxn 

-    237.0 

+    146.4 

+     103.9 

+    234.6 

83.3 

-  .     5.1 

XXIII 

-    222.1 

-      13.4 

-      15.2 

+    218.3 

-      11.5 

+      10.6 

XXIV 

+    204.2 

-      30.9 

40.0 

+        7.4 

+      20.9 

39.4 

XXV 

-    192.0 

+        7.5 

+        7.8 

+    192.5 

1.7 

+        2.1 

XXVI 

+     191.1 

+    141.0 

4-    126.8 

•     187.8 

1.4 

2.7 

xxvn 

+    162.0 

-      86.7 

+     110.3 

-     238.0 

4-      29.9 

4.7 

XXVIII 

-    148.9 

+      21.4 

+      52.2 

+    188.6 

+      13.8 

9.1 

XXIX 

+    122.3 

+      11.8 

+      11.8 

122.9 

+        4.2 

4.5 

XXX 

-      79.0 

+        5.0 

5.4 

84.8 

XXXI 

-      72.0 

+      10.1 

8.1 

-      66.4 

2.4 

+        0.9 

XXXII 

+      44.0 

+      50.4 

46.7 

+      39.6 

4.0 

+        0.9 

XXXIII 

+      32.1 

+        3.7 

+        3.5 

32.4 

+        0.8 

0.9 

XXXIV 

+      30.7 

3.5 

+        3.0 

+      29.9 

XXXV 

25.6 

3.1 

+      11.6 

1.8 

1.7 

+        2.6 

XXXVI 

21.9 

+        1.3 

1.1 

20.7 

XXXVII 

+      20.8 

+        7.2 

+      20.2 

+    113-3 

5.5 

+        8.6 

XXXVIII 

20.6 

30.8 

+      37.4 

0-0 

2.5 

+        4.9 

XXXIX 

16.8 

21.4 

-      22.0 

+      18.8 

+      15.5 

1.0 

XL 

17.7 

+        3.1 

3.0 

17.2 

XLI 

-      10.1 

+        1.9 

+        2.1 

+      10-4 

2.1 

+        0.2 

XLII 

9.4 

+      16-8 

+      15.9 

+        9.2 

1.9 

0.0 

XLIII 

8.9 

+        1.2 

+        1.2 

+        9.3 

+        4.3 

2.5 

XLIV 

7.7 

3.0 

+        5.4 

2.0 

XLV 

2.3 

11.4 

+        4.1 

17.7 

0.0 

1.6 

Tables  for  the  equation  of  the  centre  and  the  radius  vector  have  been  superseded  by  solving  KEPLER'S 
problem  in  the  manner  I  have  shown  in  Vol.  III.  No.  53  of  the  Astronomical  Journal,  viz. :  —  If  we  sup- 
pose one  of  the  radii  vectores  to  turn  uniformly  about  one  of  the  foci,  describing  therefore  the  mean  anomaly, 


21 


the  other  ra<liu>  v.  ,i..r   will  then,  in  not  very  eccentric  ellipses,  describe  nearly  the  true  anomaly.      This 
auxiliary  anomaly,  denoting  with  r',  we  have,  simply, 

cot  £  v>  =  cot  £  M. 

The  logarithm  of  the  constant  factor  -     ^  is  for  Melpomene  =  9.8078595,  and  log  p  =  0.3398226  for  the 

computation  of  the  nidi  us  vector  by  means  of  r  =      •,  ' 

1  +  «co»  a 

The  correetion  c,  to  be  added  to  v1  in  order  to  get  the  true  anomaly  »,  is  given  in  Table  IL,  with  M  as  the 
argument     For  the  construction  of  this  table  I  hud  c  developed  in  the  following  series :  — 


c  =  —  526.495  sin  M 
+  2232.957  sin  2  M 
+  819.532  sin  3  M 
-j-  245.033  sin  4  M 


e  =  +  68.825  sin  5  M 
+  18.848  sin  6  M 
-j-  5.096  sin  7  M 
-f  1.395  sin  8  M 


c  =  +  0.373  sin  9  M 
+  0.103  sin  10  M 
+  0.053  sin  II  M 


Example  for  computing  a  Place  from  the  Tables. 

1861,  Feb.  5d  5"  58"  15'  Washington  M.  T.  =  Feb.  5"  12'  Berlin  M.  T. 
We  write  down  on  a  scrap  of  paper  the  constants  to  be  used.     From  Table  V.  the  logarithms  of 


log* 
9.337800 

1  —  « 

9.807860 

0.339823 

co*  (xix) 
9.982068 

co*  (jrix) 
9.427362n 

co*  (zi  x) 
8.943100 

co*(njp) 
9.449004 

co*  (yiy) 
9.966656 

co*  (n  jr) 
9.400622n 

co*  (n  z) 
8.144356n 

9.424948 

CO*  (:i  i) 

9.984015 

and  from  Table  VI., 

A' 
105°  34'  42".6 


& 

16"  53'  23".8 


C' 
357"  O7  0".6 


log  sin  a 
9.998323 


log  lin  b 
9.985806 


log  lin  e 
9.425543 


M  =  mean  anomaly,  and  t  —  time  since  1854.0  are  taken  from  Table  I. 


M  t 

1861,      84°  42  59".56  -f  7.00068 

Feb.         8  47     3.72  0.08488 

5  days       1  25    0.60  0.01369 

5  hours            3  32.53  0.00057 
58  minutes             41.09 
15  seconds               0.17 

94  59  17.67  +7.09982 


1—  e 
1+e 


COt  ^  M 

cot  £  M  =  cot  $  t/ 


47°  29  38".8  9.962142 

59  30  30.4  9.770002 

v>       119     1     0.8 
From  Table  IL    c  -  26  10.1 

v       118  34  50.7 

cos  v  9.679789n 

e  cos  v         —0.104133  9.017589» 

1  +  cos  v  0.895867  9.952243* 

r  0.387580 


22 


Formation  of  the  Arguments  from  Talk  HI.* 


I. 

n. 

III. 

IV. 

V. 

VI. 

VII. 

VHI. 

IX. 

1861, 

237.828 

322.545 

78.202 

200.37 

162.92 

9.81 

47.26 

30.94 

153.11 

Feb. 

357.425 

6.209 

1.058 

3.63 

9.85 

21.20 

14.99 

346.07 

348.64 

5  days 

359.584 

1.001 

0.171 

0.59 

1.59 

3.42 

2.42 

357.75 

358.17 

6  hours 

359.979 

0.050 

0.008 

0.03 

.      0.08 

0.17 

0.12 

359.89 

359.91 

234.816 

329.805 

79.439 

204.62 

174.44 

34.60 

64.79 

14.65 

139.83 

XI. 

xn. 

xrii. 

XIV. 

XV. 

XVI. 

xvn. 

xvni. 

1861, 

316.03 

84.72 

131.98 

125.46 

68.40 

216.7 

268.8 

332.4 

179.2 

Feb. 

358.48 

8.78 

23.78 

16.05 

339.85 

32.6 

343.5 

27.4 

38.8 

5  days 

359.76 

1.42 

3.84 

2.59 

356.75 

5.3 

357.3 

4.4 

6.3 

6  hours 

359.99 

0.07 

0.19 

0.13 

359.84 

0.3 

359.9 

0.2 

0.3 

314.26 

94.99 

159.79 

144.23 

44.84 

254.9 

249.5 

4.4 

224.6 

XIX. 

XX. 

XXI. 

XXII. 

xxm. 

XXIV. 

XXV. 

XXVI. 

XXVII. 

1861, 

118.9 

57.1 

184.1 

309.5 

193.9 

3.3 

221.5 

71.7 

34.2 

Feb. 

8.3 

36.2 

334.7 

350.8 

355.9 

13.5 

328.5 

353.3 

359.5 

5  days 

1.3 

5.8 

355.9 

358.5 

359.3 

2.2 

354.9 

358.9 

359.9 

6  hours 

0.1 

0.3 

359.8 

359.9 

0.0 

0.1 

359.8 

0.0 

0.0 

128.6 

99.4 

154.5 

298.7 

189.1 

19.1 

184.7 

63.9 

33.6 

xxvin. 

XXIX. 

XXX. 

XXXI. 

XXXII. 

xxxin. 

XXXIV. 

XXXV. 

XXXVI. 

1861, 

278.6 

343.7 

301.4 

294.9 

356.8 

259.0 

348.7 

50.6 

26.1 

Feb. 

4.7 

331.1 

41.3 

33.6 

5.7 

322.3 

56.3 

28.5 

50.1 

5  days 

0.8 

355.3 

6.7 

5.4 

0.9 

353.9 

9.1 

4.6 

8.1 

6  hours 

0.0 

359.8 

0.3 

0.3 

0.1 

359.7 

0.5 

0.2 

0.4 

284.1 

309.9 

349.7 

334.2 

3.5 

214.9 

54.6 

83.9 

84.7 

XXXVII. 

XXXVIII. 

XXXIX. 

XL. 

XLI. 

xm. 

XLHL 

XLIV. 

XLV. 

1861, 

88.0 

203.7 

187 

226 

24 

140 

147 

166 

288 

Feb. 

22.3 

17.1 

348 

54 

338 

333 

341 

23 

26 

5  days 

3.6 

2.8 

358 

9 

357 

356 

357 

4 

4 

6  hours 

0.2 

0.1 

0 

0 

0 

0 

0 

0 

0 

> 

114.1 

223.7 

173 

289 

359 

109 

125 

193 

318 

With  these  Arguments  the  perturbations  are  computed  from  Table  IV. 


*  These  Arguments  being  expressed  in  degrees  and  decimals,  360.0,  720.0,  or  1080  0,  must  be  subtracted  when  one  of  the  sums 
is  greater  than  one  of  those  numbers. 


23 


Ti-nus  with  / 
I 
II 
III 
IV 
V 
VI 
VII 
VIM 
IX 
X 
XI 
XII 
XIII 
XIV 
XV 
XVI 
XVII 
XVIII 
XIX 
XX 
XXI 
XXII 
XXIII 
XXIV 
XXV 
XXVI 
XXVII 
XXVIII 
XXIX 
XXX 
XXXI 
XXXII 
XXXIII 
X  X  X  I  V 
XXXV 
XXXVI 
XXXVII 
XXXVIII 
XXXIX 
XL 
XLI 
XLII 
XLIII 
XLIV 
XLV 

»i 

* 

& 

+ 

ma 

me. 

41U.3 
7.vt.4 

mjt 
m. 

136.1 

UM 

73.6 
37.1 
6.1 

8.7 

22.1 
18.3 
19.1 
21.2 
8.7 

7.0 

44 
U 

3.6 
LI 

1.9 
0.6 
n.- 
M 

4:i.: 

334.7 
165.2 

1  !'.'.( 

1:1.- 

101.  !» 
•-T.-J 
30.1 

21.7 
24.2 

5.7 

7.9 
6.9 

2.8 

0.6 
0.1 
0.2 

0.9 
14) 

+ 
264.9 
liV.T.- 

WJ 

MM 

127.3 
79.7 

m» 

104.2 
12.7 

10.2 
0.9 
2.0 

U 

2.6 

U 

2.4 

1.5 
0.2 
0.3 
0.7 

U 

::•>:.- 
..-..- 

460.7 

(,-.- 

•M 

•J17.4 

37.1 
23.1 

M 

•J 

:i:!.- 

•4 

12.3 
15.6 
2.0 

:!.:, 
2.5 
11.3 
3.9 
17.0 

4.4 

0.1 
2.1 

2.7 
0^ 

+ 

.-..I'.', 

m 

9M 

10^ 

1.8 
9.9 

•4 

\A 

0.1 
l.i 
0.3 

1.0 
0.7 
0.1 

2.2 
1.2 
M 

1.0 
0.1 

50.1 
21.3 
8^ 

2.J 

19.6 
4.8 
33.9 

12.0 
0.3 
1.7 

OJ> 
34i 

0.3 

0.3 

0.4 

0.1 
!.."> 

0.2 
0.4 

cos(r,r)S,    +    4890.0 
cos  (jri  x)  ti     •       265.9 
co*  (zi  x  )  Ci    +        49.0 

» 

Reduction  to  the  appar- 
ent equinox. 

/+2o".03 
9      0    ,0.9765 
G  338  24 
sin(G+o')Hl    99.9697 
tan  »'              9.3529 
+  l'.99  oTaii'.H 
J  o'  +22.22 

coe(G  +  o)             9.5573. 
JV  -  3.42  0.5338. 

o=13245      :i.-,'.':, 
i  -  +12  42        3.4 

E     -     4603.1 

co«(r,y){i     +    1412.5 
cos  (jri  jf)  ft    +      920.2 
cot(«ij)ti    -        14U.4 

1    -I-    2192J 

CD*  (l  *)  Ei    -        70.0 
cot  (jn  «)  >n    +      264.3 
cos  (*i  *)  Ci    +      537.9 

C    +      732.2 

sin  (4'  +  r)  224°  9  33.3  9.843018. 
r  sin  a                      0.385903 
*                    0.228921. 

sin  (B1  +  r)  135  28  14.5  9.845888 
r  sin  6                      0.373386 
y                  0^i:i-'7) 

sin  (<?+  r)  115  34  51.3  9.955195 
r  sin  c                      9.813123 
*                      9.768318 

y    +1.656815 
H    +       2H>2 
Y   -0.614699 
^cosa'sina'    +1.044308  0.018828 

*    -1.694031 
J    +       4603 
X    +0.723955 
^cosa'cosa'    -0.965473  9.984740. 

•in  a'      0    ,     ,     9^65861 
tan  a'  132  45  13.3  0.034088. 

*    +0.586568 
C    +         732 
Z   -0.266747 
J  sin  *'    +0.320553  9^05900 
JcotV                      0.152967 
cos**         0    (  f    9.989240 
tan  J>    +12425^  9.352933 

J                    0.163727 

a'  and  f  arc  referred  to  the  mean 
equinox  1861.0. 

6.  <ll<  »l 

L 

MM 

+  5023.3 
.700961 

198.2 

3607.7 
+    993.6 

kitnu 

J.ll.l 

720.8 
•I-   558.1 
2.746712 

62.7 

My  computations  for  1861,  with  the  oscillating  element*  for  1854.0  and  the  special  perturbations  by  Jupiter  and  Saturn,  give 
for  the  same  time  :  — 
a  =     132  45  33.3 
*  =  +  12  42    2.0 

Ja 
Jt 

U 
1.4 

24 

By  this  close  agreement  between  the  two  different  computations,  the  correctness  of  the  tables  is  satisfactorily 
proved. 

For  the  computation  of  an  exact  opposition  ephemeris,  it  will  be  necessary  only  to  compute  the  perturbations 
from  16  to  16  days  from  the  tables,  and  then  to  interpolate  them  twice  in  the  middle,  in  order  to  get  them 
from  4  to  4  days,  with  which  interval  such  ephemerides  are  commonly  calculated.  For  an  approximate 
ephemeris  for  the  whole  year,  the  terms  multiplied  with  the  time  and  the  first  four  equations  will  be  suffi- 
cient, «nd  also  a  direct  computation  of  the  perturbations  only  from  40  to  40  days,  with  afterwards  two 
interpolations  in  the  middle,  if  the  ephemeris  is  to  be  computed  from  10  to  10  days. 


25 


TABLE    I. 

FOR   TIIK    Ml.  AN    ANOMALY. 

The  time*  are  referred  to  the  meridian  of  Washington. 

V    ,1  • 

M 

,t 

Yew*. 

M 

i 

i-.vj  /; 

1           H 

2:1:1  17  25.88 

1-77 

300°  48  :!••'. 

+23.00068 

I  -:,:! 

:i:t»;  4:1    !'.:.:  ' 

. 

1-7- 

44    8  23.22 

24.0UOOO 

I  -:.  I 

M    -  :.:i.:ii        |           0.00000 

i-;  ' 

147  34    6.93 

MJ8M 

i-:t  :i4  :t7.n:t 

9, 

1880  B 

•J.M  iti  :>o.77 

26.IHH37 

I8H  /•' 

•j-7  17  ao.-c, 

2.00137 

I--I 

354  42  34.48 

27.00C68 

1  -:,7 

:n>  i.;     i                        3.00068 

1—  J 

98    8  18.90 

28.00000 

1868 

134    8  46.89                      4.00000 

i--n 

201  34     1.92 

28.99932 

•J:t7  34  32.01                      4.1' 

1884  n 

305  16  45.75 

30.001  37 

1-1,1  /; 

nil   17  i                          6.0(il  :!7 

I—:. 

48  42  21.47 

31.00C68 

1-1,1 

84  4'J  511.56 

7.00068 

i-i, 

158    8  13.18 

B4MOO 

I-*.-.1 

I-i    8  43.88 

8.00000 

1--7 

255  33  56.90 

Mjna 

1861 

I'll  ni  2ti.'.'!i 

1  >n2 

I--H  B 

:i--!i  16  40.74 

34.0(11  :!7 

1-1,1  /; 

:f,  17  10.83 

10.001:17 

|-~i 

in.'   I-J  21.45                    35.00C68 

I86B 

in-  42  .M.  .v. 

11.00068 

l-'.ni 

-'Hi     -     -.17                      36.00000 

1866 

•JIJ    8  38.86  fc 

12.00000 

!-''! 

309  33  51.88                     36.991i:J2 

1867 

:V45  34  21.98 

12.99932 

1-2  B 

5:t   Ki  :i5.72                      :t-.i:ol37 

l-i  i-i  B 

89  17    5.81 

14.00137 

IBM 

156  42  19.44                    39.00068 

I-,.' 

I!  >2  42  49.53                    15.00063 

i-'i 

260     8     3.15                     40.00000 

1-7  1 

•j-.Hi    -  nn.-j:, 

16.00000 

I-T, 

3  33  46.87                     4I>.!I9!>32 

1-71 

j£l  IJ4   Iti.'Hi 

16.!" 

1896  B 

107  16  30.70                    42.00137 

i-7-j  /; 

II.:  17    0.80 

18.00137 

1897 

210  42  14.42                    43.00068 

1-7:: 

•JH,  42  4i.:.i 

1!U>0068 

I-,- 

314     7  58.14                      44.00000 

1-71 

350     8  2-. 

90.00000 

1-  ,•, 

57  33  41.85                     44.!'1.'!i::2 

1-7'. 

93  :n  n.'.'.-. 

20.'t9932 

1900  B 

161  16  25.(i!i                  +46.00137 

l-7ii  /( 

197  16  55.78 

+32.00137 

Month*. 

if 

l 

Day*. 

it 

t 

o     »     • 

•           il 

January 

0    0    0.00 

+0.00000 

1 

o  17    0.12 

+O.OC374 

Ki  l,niary 

8  47    3.72 

0.08488 

8 

0  34    0.24 

0.00548 

March 

16  43    7.08 

0.16154 

3 

0  51     0.36 

O.IKIH2I 

April 

•J.->  30  10.78 

0.24642 

4 

1    8    0.48 

0.01(»!i5 

May 

34    0  11 

0.32856 

5 

1  25     (1.60 

(i.oi:a;:i 

June 

42  47  18.10 

0.41344 

6 

1  42    0.72 

i  .   1643 

July 

51  17  2148 

0.49558 

7 

1  59    0.84 

0.01917 

August 

60    4  25.40 

0-58046 

8 

2  16    0.96 

O.G2I!N) 

inber 

li-  .'.I    211.12 

046534 

9 

2  :n    1."- 

O.i  2464 

i  Irtohcr 

77  21   :fj.72 

0.74748 

10 

2  50     1.20 

0.027:1* 

NoTemhoi* 

86    8  36.44 

0.83236 

93 

5  40    2.40 

d.i  5476 

Dftmber 

94  38  40.04 

+1.91450 

30 

8  :m 

+0.08214 

In  BUscxtile  Yean  one  day  most  be  subtracted  from  the  date  in  the  fir*!  two  months. 

26 


TABLE    I.  —  Concluded. 

FOR  THE   MEAN  ANOMALY. 

The  times  are  referred  to  the  meridian  of  Washington. 

Hours. 

M 

1 

Hours. 

M 

t 

1           H 

i     a 

1 

0  42.51 

+0.00011 

13 

9  12.57 

+0.00149 

2 

1  25.01 

0.00023 

14 

9  55.07 

0.00160 

3 

2    7.52 

0.00034 

15 

10  37.58 

0.00172 

4 

2  50.02 

0.00046 

16 

11  20.08 

0.00183 

5 

3  32.53 

0.00057 

17 

12    2.59 

0.00195 

6 

4  15.03 

0.00069 

18 

12  45.09 

0.00206 

7 

4  57.54 

0.00080 

19 

13  27.60 

0.00218 

8 

5  40.04 

0.00092 

20 

14  10.10 

0.00229 

9 

6  22.55 

0.00103 

21 

14  52.61 

0.00241 

10 

7    5.05 

0.00114 

22 

15  35.11 

0.00252 

11 

7  47.56 

0.00126 

23 

16  17.62 

0.00264 

12 

8  30.06 

+0.00137 

24 

17    0.12 

+0.00275 

M 

M 

For  Minutes. 

For  Seconds. 

For  Minutes. 

For  Seconds. 

1 

o".71 

o'.'oi 

31 

2K96 

0.'36 

2 

1.42 

0.02 

32 

22.67 

0.37 

3 

2.13 

0.03 

33 

23.38 

0.39 

4 

2.83 

0.05 

34 

24.09 

0.40 

5 

3.54 

0.06 

35 

24.80 

0.41 

6 

4.25 

0.07 

36 

25.50 

0.42 

7 

4.96 

0.08 

37 

26.21 

0.44 

8 

5.67 

0.09 

38 

26.92 

0.45 

9 

6.38 

0.11 

39 

27.63 

0.46 

10 

7.08 

0.12 

40 

28.34 

0.47 

11 

7.79 

0.13 

41 

29.05 

0.48 

12 

8.50 

0.14 

42 

29.76 

0.50 

13 

9.21 

0.15 

43 

30.47 

0.51 

14 

9.91 

0.16 

44 

31.17 

0.52 

15 

10.62 

0.17 

45 

31.88 

0.53 

16 

11.33 

0.19 

46 

32.59 

0.54 

17 

12.04 

0.20 

47 

33.29 

0.55 

18 

12.75 

0.21 

48 

34.00 

0.57 

19 

13.46 

0.22 

49 

34.71 

0.58 

20 

14.17 

0.23 

50 

35.42 

0.59 

21 

14.88 

0.25 

51 

36.12 

0.60 

22 

15.58 

0.26 

52 

36.83 

0.61 

23 

16.29 

0.27 

53 

37.54 

0.62 

24 

17.00 

0.28 

54 

38.25 

0.64 

25 

17.71 

0.29 

55 

38.96 

0.65 

26 

18.42 

0.31 

56 

39.67 

0.66 

27 

19.13    ' 

0.32 

57 

40.38 

0.67 

28 

19.84 

0.33 

58 

41.09 

0.68 

29 

20.54 

0.34" 

59 

41.80 

0.70 

30 

21.25 

0.35 

60 

42.51 

0.71 

'11 


TABLE    II. 

H.U  TIIK  CORRECTION  C  TO  BE  ADDED  TO  THE  AUXILIARY  ANOMALY  v1. 

Argument  ->  M.    For  J/>  180°  the  Argument  U  360°  —  31,  and  the  lign  of  c  to  be  ravened. 

Arg. 

c 

Diff. 

Arg. 

1 

Diff. 

Arg. 

c 

Diff. 

c 

Diff 

o 

1            H 

, 

0 

1       M 

„ 

o 

i        H 

, 

0 

, 

„ 

0.0 

0    0.00 

22.5 

.  Ji.    .-.-.'.I. 

45.0 

+311  29.45 

67.5 

+  8  45.17 

+  1     831 

•'"•-' 

B4 

41  9630 

•  >..! 

.5 

39    0.24 

-».3I 

68.0 

7  59.33 

-4»-84 

1.0 

2  17.58 

•.-." 

41  5338 

•.•:•"- 

46.0 

38  30.16 

30-08 

A 

7  13^7 

44.76 

A 

3  V.1..-1, 



24.0 

42  r.i.:>i 

34-81 

.5 

37  59.23 

30-93 

69.0 

6  27.'JO 

4647 

2.0 

4  :t4.79 

,,-.  .1 

i-j  4:i.»iii 

34-U 

47.0 

37  27.48 

11-76 

A 

6  42-35 

46.66 

5  43.14 

„-.!. 

25.0 

It       li..t-t 

•41 

A 

36  54.H3 

11-66 

70.0 

4  56.!'3 

46-43 

3.0 

6  5I.-T 

86.13 

A 

43  27.56 

31-31 

48.0 

36  21.61 

11-31 

.5 

4  11.65 

46-18 

A 

7  59.10 

•7-81 

26.0 

43  47.30 

19-74 

A 

35  47.54 

14-07 

71.0 

3  264>3 

46-13 

4.0 

9    6^1 

87-61 

A 

44     5.57 

18-17 

49.0 

35  12.75 

14-79 

A 

9  41.56 

44-96 

A 

10  13.75 

87-14 

27.0 

44  22.37 

16-80 

A 

34  37425 

34-50 

72.0 

1  5632 

44-76 

"<•:: 

16-33 

16-18 

44-67 

5.0 

+11  20.47 

.5 

+44  37.69 

50.0 

+34     1.07 

A 

+  1  12.25 

1:2  -J6.74 

+•8.17 

28.0 

44  .M..-.., 

+11-87 

A 

33  24425 

-M-M 

73.0 

+  0  27.90 

-44-16 

6.0 

13  32.50 

86-78 

A 

45    3.96 

11-40 

51.0 

324630 

17-46 

A 

-  0  16423 

44-11 

1  1  :!7.71 

•6-31 

29.0 

45  14.90 

10-94 

A 

32    8.74 

18-08 

74.0 

1     0.13 

41  90 

7.0 

15  4:2.3:1 

'•'•'': 

A 

45  24.40 

9-60 

52.0 

31  30.10 

18-84 

A 

1  43.78 

41-66 

16  46.31 

•3-98 

30.0 

45  32.46 

8-08 

.5 

30  50.90 

19-10 

75.0 

2  27.17 

43-39 

8.0 

17  49.61 

81-JO 

A 

45  39.07 

8-61 

53.0 

30  11.17 

19-71 

A 

3  10.29 

41-11 

A 

18  52.20 

81.69 

31.0 

45  44.27 

6-30 

A 

29  30.93 

40-34 

76.0 

3  53.12 

43-81 

9.0 

1  •  54.04 

61-84 

A 

45  48.04 

1-T7 

54.0 

28  50.19 

40-74 

A 

4  35.67 

43-66 

A 

.'  i  55.08 

61-04 

32.0 

45  5ii.4ii 

3.M 

A 

98    8.99 

41-30 

77.0 

5  17.91 

43-34 

80-10 

+  0-88 

41-63 

41-91 

10.0 

+21  55.28 

.5 

+45  51.38 

55.0 

+27  27.36 

A 

-  5  5934 

.5 

2254.61 

+69-11 

33.0 

4650.97 

-  0-41 

A 

26  45.30 

-43-08 

78.0 

6  41.45 

-4141 

ll.n 

23  53.03 

68-41 

A 

45  49.19 

1-78 

56.0 

26    234 

43-46 

A 

7  22.73 

41-38 

.5 

24  50.51 

67-48 

34.0 

45  46.05 

1-14 

A 

25  20.01 

43-81 

79.0 

8    3.66 

40-91 

12-0 

17.02 

68-61 

A 

45  41.57 

4-4* 

57.0 

24  3632 

41-19 

A 

8  44.24 

40-68 

J 

26  42-51 

66.49 

35.0 

45  35.76 

6-81 

A 

23  53.31 

41-41 

80.0 

9  24.46 

40-31 

13.0 

27  36-96 

64-41 

A 

45  28.65 

7-11 

58.0 

23    9.48 

41-81 

A 

10    4.31 

19-86 

A 

28  30.33 

61-17 

36.0 

45  20.23 

8-U 

A 

22  25.37 

44-11 

81.0 

10  43.79 

19-48 

14.0 

29  22.60 

M-*7 

A 

45  10.53 

9-70 

59.0 

21  404)9 

M-H 

.5 

11  2238 

19-08 

30  13.73 

61-11 

37.0 

44  69.58 

10-96 

A 

90  56-37 

44-81 

82.0 

12    1.57 

19-69 

49-97 

11-19 

44-86 

38-10 

154 

+31     3.70 

.5 

+44  47.39 

60.0 

+20  11.52 

A 

-123937 

.5 

31  52.48 

+48-7S 

>.ii 

44  33.97 

-11-43 

.5 

19  26.47 

-46-06 

83.0 

13  17.76 

-17.89 

lli.il 

3940.04 

47-68 

A 

44  19.35 

14-63 

61.0 

18  41.24 

44-11 

A 

13  55.23 

17*47 

.5 

XI  26.36 

46-3-1 

39.0 

44    3-55 

16.90 

A 

17  55.84 

46-40 

.-l.ii 

14  32429 

17-06 

17.0 

34  11.42 

46-08 

A 

43  46.58 

18-97 

62.0 

17  10.30 

46-64 

.5 

15    8.92 

lti-63 

J 

34  .V,.l:' 

41-77 

40.0 

43  28.48 

18-10 

.5 

16  24.63 

46-67 

85.0 

15  45.11 

18-18 

18.0 

3.-.  37.66 

41-47 

A 

43    9425 

19-H 

63.0 

15  3836 

46-77 

A 

16  2036 

16-76 

.5 

36  1830 

41-14 

41.0 

42  48.93 

30-13 

.5 

14  53.01 

46-86 

86.0 

16  56.17 

16-11 

19.0 

36  58.60 

T..-I 

42  27.52 

31-41 

64.0 

14    7.H- 

46-91 

A 

17  31.03 

14-88 

A 

37  37.03 

18-41 

42.0 

42    5.07 

33-46 

A 

13  21.11 

46-97 

87.0 

18    5.43 

14-40 

1746 

H-49 

46-01 

tt-94 

20.0 

+38  14.08 

A 

+41   11.-.- 

65.0 

+12  35.10 

A 

-18  39.37 

_5 

38  49.75 

+16-87 

43.0 

41  17.08 

-*4-80 

.5 

11  49.07 

-4841 

88.0 

19  1-J.-5 

-M-48 

21.0 

39  24.01 

14-18 

A 

40  51.60 

.''..  !- 

66.0 

11     3.05 

4841 

A 

19  4535 

33.1(1 

•5 

39  56.85 

31-84 

44.0 

40  25.15 

36-4S 

A 

10  17.05 

46-00 

89.0 

20  18.38 

11-61 

22.0 

40  29.27 

11-41 

A 

39  57.76 

97-19 

67.0 

9  31.08 

46-97 

A 

20  50.42 

32-04 

+40  58.26 

+49-99 

I5.il 

+39  29.45 

-M.11 

A 

+  8  45.17 

-46-91 

90.0 

-21  21.98 

-11-66 

28 


TABLE    II.  —  Concluded. 

FOR  THE  CORRECTION  c  TO  BE  ADDED  TO  THE  AUXILIARY  ANOMALY  v'. 

Argument  =  M.    For  J/>  180°  the  Argument  is  360°  —  M,  and  the  sign  of  c  to  be  reversed. 

Arg. 

c 

Diff. 

Arg. 

c 

Diff. 

Arg. 

c 

Diff. 

Arg. 

c 

Diff 

o 

i     ii 

u 

o 

i     » 

u 

o 

i      u 

u 

o 

i     H 

ii 

90.0 
.5 

-21  21.98 
21  53.05 

-31.07 

112.5 
113.0 

-36    9.15 
36  16.91 

-  7-76 

135.0 
.5 

-34  18.97 
34    6.94 

+12-03 

157.5 
158.0 

-20  16.21 
19  51.85 

+24-36 

91.0 

22  23.63 

30-58 

.5 

36  24.18 

7-27 

136.0 

33  54.55 

12-39 

.5 

19  27.32 

24-53 

.5 

22  53.72 

30-09 

114.0 

36  30.94 

6-76 

.5 

33  41.80 

12-75 

159.0 

19    2.61 

24-71 

92.0 

23  23.31 

29-59 

.5 

36  37.20 

6  26 

137.0 

33  28.70 

13-10 

.5 

18  37.73 

24-68 

.5 

23  52.40 

29-09 

115.0 

36  42.97 

5-77 

.5 

33  15.25 

13-45 

160.0 

18  12-68 

25-05 

93.0 

24  20.98 

28-58 

.5 

36  48.25 

5.28 

138.0 

33    1.46 

13-79 

.5 

17  47-47 

25-21 

.5 

24  49.05 

28-07 

116.0 

36  53.03 

4-78 

.5 

32  47.32 

14-14 

161.0 

17  22-10 

25-37 

94.0 

25  16.62 

27-57 

.5 

36  57.33 

4-30 

139.0 

32  32.85 

14-47 

.5 

16  56-58 

25-52 

.5 

25  43.67 

27-05 

117.0 

37    1.14 

3-81 

.5 

32  18.04 

14-81 

162.0 

16  30-90 

25-68 

26-54 

3-32 

15-14 

25-82 

95.0 

-26  10.21 

.5 

-37    4.46 

140.0 

-32    2.90 

.5 

-16    5.08 

.5 

26  36-24 

-26-03 

118.0 

37    7.31 

-  2-85 

.5 

31  47.44 

+  15-46 

163.0 

15  39.11 

+25-97 

96.0 

27     1.75 

28-51 

.5 

37    9.67 

2-36 

141.0 

31  31.65 

15-79 

.5 

15  13.00 

26-11 

1«8S 

16-10 

26-24 

.5 

27  26.74 

:j4-yy 

119.0 

37  11.55 

.5 

31  15.55 

164.0 

14  4G.7G 

97.0 

27  51.20 

24-46 

.5 

37  12.97 

1-42 

142.0 

30  59.13 

16-42 

.5 

14  20.38 

26-38 

.5 

23  15.14 

23.94 

120.0 

37  13.91 

0-94 

.5 

30  42.41 

16-72 

165.0 

13  53.68 

26-50 

98.0 

28  38.56 

23-42 

.5 

37  14.38 

0-47 

143.0 

30  25.37 

17-04 

.5 

13  27.25 

26-63 

.5 

29     1.45 

22-89 

121.0 

37  14.39 

-  0-01 

.5 

30    8.04 

17-33 

166.0 

13    0.51 

26-74 

99.0 

29  23.82 

22-37 

.5 

37  13.93 

+  0-40 

144.0 

29  50.41 

17-63 

.5 

12  33.65 

26-86 

.5 

29  45.66 

21-84 

122.0 

37  13.01 

0-92 

.5 

29  32.48 

17-93 

167.0 

12    6.68 

26-97 

21-32 

1-37 

18-22 

27-07 

100.0 

-30    6.98 

.5 

-37  11.64 

145.0 

-29  14.26 

.5 

-11  39.61 

.5 

30  27.77 

-20-79 

123.0 

37    9.81 

+  l.RS 

.5 

23  55.75 

+18-51 

168.0 

11  12.43 

+27-18 

101.0 

30  48.03 

20-26 

.5 

37    7.53 

2.28 

146.0 

28  36.96 

18-79 

.5 

10  45.15 

27-28 

.5 

31     7.76 

19-73 

124.0 

37    4.81 

2-72 

.5 

28  17.89 

19-07 

169.0 

10  17.78 

27-37 

102.0 

31  26.97 

19-21 

.5 

37     1.64 

3-17 

147.0 

27  58.54 

19-35 

.5 

9  50.32 

27-46 

.5 

31  45.64 

18-67 

125.0 

36  58.04 

3-60 

.5 

27  38.93 

19-61 

170.0 

9  22.77 

27-55 

103.0 

32    3.79 

18-15 

.5 

36  54.00 

4-04 

148.0 

27  19.05 

19-88 

.5 

8  55.14 

27-63 

.5 

32  21.41 

17-62 

126.0 

36  49.53 

4-47 

.5 

26  58.91 

20-14 

171.0 

8  27.43 

27-71 

104.0 

32  38.50 

17-09 

.5 

36  44.63 

4-90 

149.0 

26  38.51 

20-40 

.5 

7  59.64 

27-79 

.5 

32  55.06 

16-56 

127.0 

36  39.31 

5-3-2 

.5 

26  17.86 

20-65 

172.0 

7  31.79 

27-85 

16-04 

5-74 

20-90 

27-92 

105.0 

-33  11.10 

.5 

-36  33.57 

150.0 

-25  56.96 

.5 

-  7    3.87 

.5 

33  26.61 

-15-51 

123.0 

36  27.41 

+  6-16 

.5 

25  35.81 

+21.15 

173.0 

6  35.89 

+27-98 

106.0 

33  41.59 

14-98 

.5 

36  20.83 

6-58 

151.0 

25  14.41 

21-40 

.5 

6    7.85 

28-04 

.5 

33  56.05 

14-46 

129.0 

36  13.84 

6.99 

.5 

24  52.78 

21-63 

174.0 

5  39.76 

28-09 

107.0 

34     9.99 

13-94 

.5 

36    6-44 

7-40 

152.0 

24  30.92 

21-86 

.5 

5  11.62 

28-14 

.5 

34  23.40 

13-41 

130.0 

35  58.63 

7-81 

.5 

24     8.83 

22-09 

175.0 

4  43.44 

28-18 

108.0 

34  36.30 

12-90 

.5 

35  50.41 

8-22 

153.0 

23  46.51 

22-32 

.5 

4  15.21 

28-23 

.5 

34  48.68 

12-38 

131.0 

35  41.80 

8-61 

.5 

23  23.98 

22-53 

176.0 

3  46.94 

28-27 

109.0 

35    0.54 

11-86 

.5 

35  32.79 

9-01 

154.0 

23    1.23 

22-75 

.5 

3  18.65 

2S-29 

.5 

35  11.88 

11-34 

132.0 

35  23.39 

9-40 

.5 

22  38.27 

22-96 

177.0 

2  50.32 

28-33 

10-83 

9-79 

23-17 

28-35 

110.0 

-35  22.71 

.5 

-35  13.60 

155.0 

-22  15.10 

.5 

-  2  21.97 

.5 

35  33.02 

-10-31 

133.0 

35    3.43 

+10-17 

.5 

21  51.72 

+23-38 

173.0 

1  53.60 

+28-37 

111.0 

35  42.82 

9-80 

.5 

34  52.87 

10-56 

156.0 

21  28.14 

23-58 

.5 

1  25.21 

28-39 

.5 

35  52.10 

9-28 

134.0 

34  41.94 

10-93 

.5 

21     4.36 

23-78 

179.0 

0  56.81 

28-40 

112.0 

36    0.88 

8-78 

.5 

34  30.64 

11-30 

157.0 

20  40.38 

23-98 

.5 

-  0  28.41 

28-40 

.5 

-36    9.15 

-  8.27 

135.0 

-34  18.97 

+11-67 

.5 

-20  16.21 

+24-17 

180.0 

0    0.00 

+28-41 

29 


TABLE    III. 

FOR  THE   AR<il  Ml.NTS. 

A.    For  the  different  Tears.    The  times  are  referred  to  the  meridian  of  Washington. 

Yea™. 

1 

II. 

III. 

IV. 

V. 

VI. 

VII 

VIII. 

IX 

1858  B 

. 

24°.2I4 

32&061 

175.14 

'.35 

381°73 

!457°.60 

68°56 

377J3 

r.'  . 

"7.:tl7 

,,1:1 

M 

:i  15.23 

17l.:i5 

74.04 

264.48 

14:».- 

1-M 

I7o.  I-.M 

KO8M 

960.1,  ' 

71.11 

60.09 

-.'.7 

100.  in 

m.ia 

:.-'.•>  i: 

3.418 

303.47 

187.00 

310.63 

67.10 

2%.:ia 

236.37 

i--.<;  n 

.  .:t:i 

316.8% 

1  5.H05 

346.37 

303.1!) 

2»X'."I 

244.12 

nun 

loa.a.-, 

I-.-.7 

:i5i>.ai:i 

mm 

a8.:c,7 

29.  14 

.-,....7 

327.71 

:i-.-.:.'i 

wet 

MMM 

4U.8IO 

174.1*6 

340.22 

237.18 

163.63 

194.74 

i  •  ' 

562 

17ti.i:i- 

53.963 

114.70 

290.84 

229.85 

53.71 

359.55 

li  v.io 

I860  D 

i.-.i 

MiVMI 

749 

1.-.7.59 

47.04 

iai.17 

230.73 

1  '.'..OS 

•J-I..-7 

l-(,l 

:.-<28 

78.202 

200.37 

1'.. 

!•.-! 

47.26 

HUM 

1.VI.11 

1-..-J 

207.503 

35.64H 

90^54 

243.15 

278.80 

259.44 

223.7:i 

326.86 

MJ6 

1863 

177.178 

i  -.:  .• 

.108 

885.!  i.l 

34.68 

149.08 

40.33 

tut 

245.60 

1-61  11 

1  H..769 

182.056 

11 

328.82 

1MI.88 

::".!" 

217.34 

•MB 

111.48 

1-.,-, 

llii.444 

255.1  Vi 

128.047 

11.60 

266.76 

389.03 

33^7 

94.17 

337.7:1 

I-,,, 

86.119 

323.263 

140.500 

64.:W 

22.64 

178.67 

210.41 

290.00 

2rej.!>7 

]-<,: 

man 

41.366 

152. 

97.16 

138.53 

68.30 

KM 

126.01 

nM 

186-  /; 

•-T..3S5 

114.670 

165.440 

140.05 

254.72 

31H.62 

203.05 

321.48 

296.10 

1869 

:i55.o60 

l'.'7.774 

177. 

182.83 

10.62 

208.26 

20.49 

157.41 

162.35 

1-7. 

:;•.'!.  734 

260-877 

190.346 

225.01 

126.49 

97.90 

197.02 

353.33 

BAH 

i-;i 

294.409 

333.981 

902.79'.) 

268.39 

242.37 

:U7..V! 

1U6 

189.25 

254.84 

i-;-.'  /; 

264.001 

47.284 

-.'  15.286 

311.29 

:i:.-..-,7 

237.85 

190  .57 

24.72 

12.t.7-_' 

1-7:1 

.U76 

120.388 

337.740 

354.06 

114.45 

127.49 

7.10 

220.64 

346.% 

1-71 

-.'•a.350 

193.492 

240.  loa 

36.84 

230.33 

17.12 

183.63 

56.56 

213.21 

1-7.-. 

173.025 

252.646 

79.62 

346.22 

266.76 

0.17 

252.48 

79.46 

1-76  D 

1  lv!.617 

339.899 

265.134 

122.52 

102.42 

157.08 

177.18 

87.95 

305.34 

1-77 

112.2<K2 

53.003 

277.586 

1G5.29 

218.30 

.n;.7-j 

:»53.7I 

283^7 

171.58 

1878 

81.967 

126.107 

290.040 

208.07 

334.18 

296.35 

170.25 

119.80 

::7.-l 

1-7' 

f,  1.642 

199.210 

302.494 

250.85 

90.06 

185.00 

346.78 

315.71 

264.07 

l-s)  B 

a  1.234 

272.514 

314.981 

293.74 

206.26 

76.30 

163.80 

151.19 

129.95 

1881 

350.906 

345.618 

327.434 

336.5:! 

322.14 

325.95 

340.33 

347.11 

356.30 

1—  .' 

.583 

58.721 

339.887 

19.30 

78.02 

215.58 

156.86 

183.03 

222.44 

l-i 

290.258 

131.825 

Il.VJ.340 

62.08 

103.91 

105.22 

333.39 

18.95 

88.69 

1834  n 

.-149 

205.129 

4.827 

104.98 

310.11 

355.54 

150.41 

214.4a 

314.57 

1--.-, 

229..V-M 

278.232 

17.2SO 

147.76 

C5.!tO 

245.17 

326.04 

50.34 

180.82 

I--., 

100.198 

351.335 

20.732 

190J-,:i 

181.87 

134.81 

143.47 

246.26 

47.06 

1-7 

168.873 

64.439 

42.185 

233.31 

207.75 

24.44 

330.00 

-.M- 

27:1.31 

1*8  B 

138.465 

137.743 

54.672 

276.ai 

53.95 

274.76 

137.02 

277.65 

139.19 

1-, 

108.139 

210.846 

67.125 

318.98 

169.83 

164.40 

M 

113.58 

5.43 

18M 

77.814 

283.950 

70.578 

1.76 

385.71 

54.03 

130.09 

300.40 

231.68 

i->i 

47.489 

357.ar>3 

92.031 

44.54 

dJD 

303.67 

306.62 

145.41 

97.92 

1*92  B 

17.080 

?o.:v,7 

104.517 

87.44 

157.79 

193.99 

121.63 

340.88 

323.80 

1-  •: 

346.755 

143.460 

116.070 

130.23 

273.68 

-::.i,.! 

300.17 

176^1 

190.05 

1-  '! 

316.430 

216.564 

129.423 

172.99 

•-"..v; 

333.26 

116.70 

12.73 

56.30 

I-'C, 

286.104 

•Meg 

141.876 

215.77 

145.44 

222.90 

293.23 

BUB 

282~r>4 

1896  fl 

255.696 

2.JI71 

I.-V4.363 

358.67 

261.64 

113.22 

110.2.5 

44.12 

148.42 

1897 

225.371 

76.075 

166.816 

301.40 

i7..-,a 

2.85 

386.78 

240.04 

14.67 

1-,- 

105.045 

140.178 

179.268 

344.22 

133.30 

252.40 

103.31 

75.96 

240.01 

1899 

164.720 

MM 

191.721 

27.00 

249.28 

142.12 

279.84 

271.88 

107.16 

1900  fl 

134.IU  1 

a  n.  aw 

5.48 

32.44 

107.35 

333.04 

30 


TABLE    III.—  Continued. 

•  FOR  THE   AEGUMENTS. 

A.     For  the  different  Years.     The  times  are  referred  to  the  meridian  of  Washington. 

Years. 

X. 

XI. 

XII. 

XIII. 

XIV. 

XV. 

XVI. 

XVII. 

XVIII. 

1852  B 

116°.98 

233°.29 

130.80 

223°57 

44^34 

o 
4.1 

219.5 

305.9 

o 
28.3 

1853 

99.11 

336.72 

50.76 

52.55 

167.16 

27.5 

25.1 

268.7 

124.8 

1854 

81.24 

80.15 

330.72 

241.53 

289.98 

50.9 

190.7 

231.4 

221.3 

1855 

63.37 

183.58 

250.68 

70.52 

52.79 

74.3 

356.3 

194.1 

317.8 

1856  B 

45.44 

267.29 

171.41 

260.02 

174.06 

98.7 

161.3 

157.8 

55.5 

1857 

27.57 

30.72 

91.37 

89.01 

297.78 

122.1 

326.9 

120.5 

152.0 

1858 

9.70 

134.15 

11.33 

277.99 

60.59 

145.5 

132.5 

83.3 

248.5 

1859 

351.82 

237.58 

291.29 

1(56.98 

183.41 

168.9 

2D8.1 

46.0 

345.0 

186t)  B 

333.90 

341.29 

212.02 

296.48 

305.58 

193.3 

103.2 

9.6 

82.7 

1861 

316.03 

84.72 

131.98 

125.46 

68.40 

216.7 

268.8 

332.4 

179.2 

1862 

298.16 

188.15 

51.94 

314.45 

191.21 

240.1 

74.4 

295.1 

275.7 

1863 

280.29 

291.57 

331.90 

143.43 

314.03 

263.5 

240.0 

257.8 

12.2 

1864  B 

262.36 

35.29 

252.63 

332.93 

76.20 

287.9 

45.0 

221.5 

1.10.0 

1865 

244.49 

138.72 

172.59 

161.92 

199.01 

311.3 

210.6 

184.2 

2C6.5 

1866 

226.62 

242.14 

92.55 

350.91 

321  .,83 

334.7 

16.2 

146.9 

303.0 

1867 

208.75 

345.57 

12.51 

179.89 

84.65 

358.1 

181.8 

109.7 

39.5 

1868  B 

190.82 

89.29 

293.24 

9.39 

206.81 

22.5 

346.9 

73.3 

137.2 

1869 

172.95 

192.71 

213.20 

198.38 

329.63 

45.9 

152.5 

36.0 

233.7 

1870 

155.08 

296.14 

133.16 

27.37 

92.45 

69.3 

318.1 

ar>8.8 

330.2 

1871 

137.21 

39.57 

53.12 

216.35 

215.27 

92.7 

123.7 

321.5 

66.7 

1872  B 

119.29 

143.28 

333.85 

45.85 

337.43 

117.1 

288.7 

285.1 

164.4 

1873 

101.42 

246.71 

253.81 

234.84 

100.25 

140.5 

94.3 

247.9 

260.9 

1874 

83.54 

350.14 

173.77 

63.83 

223.07 

163.9 

259.9 

210.6 

357.4 

1875 

65.67 

93.57 

93.74 

252.81 

345.89 

187.3 

65.5 

173.4 

93.9 

1876fi 

47.75 

197.28 

14.46 

82.32 

108.05 

211.7 

230.6 

137.0 

191.6 

1877 

29.88 

300.71 

294:42 

271.30 

230.87 

235.1 

36.2 

99.7 

288.1 

1878 

12.01 

44.14 

214.39 

100.29 

353.69 

258.5 

201.8 

62.5 

24.6 

1879 

354.13 

147.57 

134.35 

289.27 

116.50 

281.9 

7.4 

25.2 

121.1 

1880  B 

336.21 

251.28 

55.08 

118.78 

238.67 

306.3 

172.4 

348.8 

218.9 

1881 

318.34 

354.71 

335.04 

307.76 

1.49 

329.7 

338.0 

311.6 

315.4 

1882 

300.47 

98.14 

255.00 

136.75 

124.31 

353.1 

143.6 

274.3 

51.9 

1883 

282.60 

201.57 

174.96 

325.73 

247.12 

16.5 

309.2 

237.0 

148.4 

1884  B 

264.68 

305.28 

95.69 

155.23 

9.29 

41.0 

114.3 

200.7 

246.1 

1885 

246.80 

48.71 

15.65 

344.22 

132.11 

64.4 

279.9 

163.4 

342.6 

1886 

228.93 

152.14 

295.61 

173.20 

254.92 

87.7 

85.5 

126.1 

79.1 

1887 

211.06 

255.57 

215.57 

2.19 

17.74 

111.1 

251.1 

88.9 

175.6 

1888  B 

193.14 

359.28 

136.30 

191.69 

139.91 

135.6 

56.1 

52.5 

273.3 

1889 

175.26 

102.71 

56.26 

20.68 

262.73 

159.0 

221.7 

15.2 

9.8 

1890 

157.39 

206.14 

336.22 

209.66 

25.54 

182.4 

27.3 

338.0 

106.3 

1891 

139.52 

309.56 

256.18 

38.65 

148.36 

205.7 

192.9 

300.7 

202.8 

1892  B 

121.60 

53.28 

176.91 

228.15 

270.53 

230.2 

358.0 

264.3 

300.5 

1893 

103.73 

156.71 

96.87 

57.14 

33.34 

253.6 

163.6 

227.1 

37.0 

1894 

85.85 

260.13 

16.83 

246.12 

156.16 

277.0 

329.2 

189.8 

133.5 

1895 

67.98 

3.56 

296.79 

75.11 

278.98 

300.4 

134.7 

152.6 

230.0 

1896  B 

50.06 

107.28 

217.52 

264.61 

41.15 

324.8 

299.8 

116.2 

327.8 

1897 

32.19 

210.70 

137.48 

93.59 

163.96 

348.2 

105.4 

78.9 

64.3 

1898 

14.31 

314.13 

57.44 

282.58 

236.78 

11.6 

271.0 

41.7 

160.8 

1899 

356.44 

57.56 

337.40 

111.56 

49.60 

35.0 

76.6 

4.4 

257.2 

1900  B 

338.52 

161.27 

258.13 

301.07 

171.76 

59.4 

241.7 

328.0 

355.0 

31 


TABLE    III.  —  Gmtbuud. 

mi;  TIII:  AUGI-.MKNTS. 

A.    For  the  different  Yeui.    The  time*  are  referred  to  tho  meridian  of  Washington. 

Twn. 

\1  \ 

\\ 

\\I 

XXII 

\\lll 

XX1\ 

XXV. 

XXVL 

XXVII 

o 

o 

O 

o 

O 

•          o 

o 

o 

l-v_-  /; 

:tli,.:i 

17  '.-.' 

MU 

MM 

867.9 

14.5 

322.0 

58.8 

83.0 

MJ 

MM 

i-.i 

MM 

ttft.7 

173.1 

311.0 

340.3 

77.6 

I-.M 

I.VJ.I 

:tn.ti 

MM.:, 

352.1 

171.:. 

331.8 

300.0 

261.8 

IM 

MM 

17.7 

172.7 

123.3 

130.5 

MM 

MJ 

1  -.  ,6  B 

::i-.i; 

-.'..I 

234.0 

134.1 

75.0 

MM 

277.2 

104.5 

61.3 

1-57 

r.i.-j 

396.2 

•-'.-..•.' 

26.8 

68.2 

MM 

26.0 

55.9 

MM 

1-1.7 

217.4 

:i:.-.i 

MM 

MM 

MM 

255.3 

307.5 

50.5 

tan 

•--.'.  7 

MM 

60.5 

167.5 

290.4 

•TV, 

244.4 

MM 

45.1 

letxi  /; 

.".  ' 

1-JI.'' 

:.-.  i 

242.1 

204.6 

•-•:  :•.'.! 

150.2 

39.7 

tan 

iias 

.-,7.1 

184.1 

MM 

193.9 

3.3 

221.5 

71.7 

34.2 

I-.-.- 

•JI7.il 

MM 

MM 

200.7 

145.7 

162.0 

210.6 

353.2 

28.8 

URJ 

I-.M 

3U-.I 

91.8 

97.5 

MM 

199.6 

274.6 

23.4 

1864  /; 

Mil 

:;,,'.  7 

342.7 

49.1 

1  19.7 

187.7 

195.9 

18.0 

1-,,-, 

151.3 

71.  i 

233.8 

0.9 

278.4 

176.7 

117.4 

12.5 

29.1 

134.1 

125.0 

312.7 

77.0 

11,:..- 

38.9 

7.1 

1867 

95.2 

16.1 

264.5 

235.7 

1.  M.'i 

320.3 

1.7 

1868  B 

-.-..'. 

MM 

•J-.7.I, 

267.0 

216.2 

34.8 

MM 

241.6 

356.3 

Ml 

183.6 

MB.? 

B9.7 

l.-.-.l 

MM 

193.4 

132.0 

163.1 

350.8 

1-7U 

MU 

mj 

21.9 

49.3 

119.8 

352.1 

121.0 

MJ 

:vi.-,.4 

1-71 

I''.'. 

1.1 

84.1 

300.4 

71.6 

150.8 

110.1 

6.0 

340.0 

1-7-2  D 

117.9 

o.i 

1  1:..  1 

191.3 

23.3 

309.9 

98.2 

MM 

334.6 

l-7:i 

m&ja 

134.6 

207.G 

--M 

335.I 

in-.:, 

87.2 

MM 

329.2 

1-71 

:ti:t.'i 

2no.8 

333.6 

MM 

267.2 

76.3 

130.2 

323.7 

1  -7.-, 

'.1.  •• 

•j  9 

MJ1 

224.7 

238.7 

65.8 

65.3 

51.7 

318.3 

1-76  B 

334.3 

33.3 

115.G 

190.4 

224.9 

53.4 

333.0 

:u  •_>.!• 

1-77 

.'I-..' 

40.4 

95.5 

6.8 

142.2 

23.6 

42.5 

254.5 

307.5 

1-7- 

346.2 

106.6 

mjs 

a-.7.ii 

94.0 

182.3 

31.5 

17:..  ' 

302.0 

1-7' 

-I.-.' 

17-J.- 

140.0 

45.8  • 

340.9 

20.6 

97.4 

296.6 

l-*0  D 

1-.'.-. 

240.1 

281.1 

39.9 

357.5 

140.0 

8.6 

18.7 

291.2 

1-1 

MJ 

343.3 

MU 

309.3 

298.7 

357.7 

300.2 

MM 

1—  .' 

18.5 

12.4 

4r..-> 

182.2 

261.1 

97.3 

346.8 

221.6 

260.4 

l-l 

IMU 

78.6 

107.6 

7:1.4 

212.9 

256.0 

335.8 

143.1 

274.9 

1884  fi 

•Jll.- 

II.V' 

169.0 

324.2 

164.5 

.-,-,.! 

323.9 

64.4 

26!  1.5 

1---. 

KU 

212.1 

231.2 

2I.-..4 

116.3 

213.7 

318.9 

345.9 

264.1 

!--.; 

293.3 

KKi.r, 

(,-.! 

12.4 

302.0 

267.3 

1-7 

148.8 

344.4 

av,.:, 

357.7 

MJ 

171.1 

291.0 

1-.- 

253.2 

1888  B 

247.1 

51.8 

:..,.- 

248.5 

331.6 

330.2 

279.1 

110.1 

247.8 

1889 

MB.1 

ll-.'i 

HM 

139.7 

283.4 

!•„'-.- 

268.2 

31.5 

242.4 

UN 

83.1 

184.1 

i-i.-j 

30.8 

23.J.2 

MTJ 

257.2 

313.0 

237.0 

MM 

181.1 

250.3 

243.3 

MM 

187.0 

86.1 

246.3 

Mtfi 

231.5 

1892  B 

279.4 

317.6 

304.7 

172.8 

U-.7 

245.2 

234.3 

MM 

226.1 

1893 

17.4 

6.9 

64.0 

903 

43.!» 

•."."..I 

77.2 

220.7 

1894 

II.  '..I 

90.0 

69.0 

315.1 

42.3 

202.6 

212-5 

358.7 

215.3 

1  -  15 

213.4 

r.',.i 

131.2 

•j  .,.: 

354.1 

1.2 

201.5 

MM 

209.9 

1896  fi 

311.7 

MM 

97.1 

305.8 

160.3 

MM 

201.4 

MM 

1897 

49.7 

'.-  Mi 

254.7 

MM 

257.6 

319.0 

178.6 

MU 

199.0 

1898 

147.7 

MM 

316.9 

239.4 

209.4 

117.0 

167.7 

44.4 

UM 

1899 

245.7 

62.0 

19.0 

130.6 

161.2 

27G.3 

156.8 

188.2 

1900  B 

344.0 

!•_".:! 

8-1.1 

Sl.fi 

I  !•-.'.- 

7r,.4 

11!.- 

247.1 

1  -.'.7 

32 


TABLE    III.—  Continued. 

FOR  THE   ARGUMENTS. 

A.    For  the  different  Years.     The  times  are  referred  to  the  meridian  of  Washington. 

Years. 

XXVIII. 

.  XXIX. 

XXX. 

XXXI. 

XXXII. 

XXXIII. 

XXXIV. 

XXXV. 

XXXVI. 

o 

o 

o 

o 

O 

o 

0 

O 

1852  B 

141.2 

171.1 

237.4 

330.1 

107.3 

297.8 

134.9 

272.0 

110.7 

1853 

196.4 

190.4 

4.2 

6.0 

174.9 

213.7 

78.2 

247.2 

340.9 

1854 

251.7 

209.7 

131.0 

41.8 

242.6 

129.7 

21.6 

222.4 

211.2 

1855 

306.9 

229.2 

257.8 

77.7 

310.3 

45.6 

324.9 

197.6 

81.4 

1856  B 

2.3 

247.7 

26.0 

114.6 

18.2 

320.4 

270.1 

173.7 

313.3 

1857 

57.5 

267.1 

152.8 

150.4 

85.9 

236.3 

213.5 

148.9 

183.5 

1858 

112.7 

286.4 

279.6 

186.3 

153.5 

152.3 

156.8 

124.1 

53.8 

1859 

168.0 

305.8 

46.4 

222.1 

221.2 

68.3 

100.2 

99.3 

284.0 

I860  B 

223.4 

324.3 

174.6 

259.1 

289.1 

343.0 

45.3 

75.4 

155.9 

1861 

278.6 

343.7 

301.4 

294.9 

356.8 

259.0 

348.7 

50.6 

26.1 

1862 

333.8 

3.1 

68.2 

330.7 

64.5 

174.9 

292.0 

25.7 

256.4 

1863 

29.0 

22.5 

195.0 

6.6 

132.1 

90.9 

235.4 

0.9 

126.6 

1864  B 

84.4 

40.9 

323.2 

43.5 

200.0 

5.6 

180.5 

337.0 

358.5 

1865 

139.6 

60.3 

90.0 

79.4 

267.7 

281.6 

123.9 

312.2 

228.7 

1866 

194.9 

79.7 

216.8 

115.2 

335.4 

197.5 

67.2 

287.4 

99.0 

1867 

250.1 

99.1 

343.7 

151.0 

43.1 

113.5 

10.6 

262.6 

329.2 

1868  B 

305.5 

117.5 

111.8 

188.0 

110.9 

28.2 

315.8 

238.7 

201.1 

186!) 

0.7 

136.9 

238.6 

223.8 

178.6 

304.2 

259.1 

213.9 

71.3 

1870 

56.0 

156.3 

5.4 

259.7 

246.3 

220.2 

202.5 

189.1 

301.6 

1871 

111.2 

175.7 

132.3 

295.5 

314.0 

136.1 

145.8 

164.3 

171.8 

1872  B 

166.6 

194.1 

260.4 

332.4 

21.9 

50.9 

91.0 

140.4 

43.7 

1873 

221.8 

213.5 

27.2 

8.3 

89.5 

326.8 

34.3 

115.6 

274.0 

1874 

277.0 

232.9 

154.1 

44.1 

157.2 

242.8 

337.7 

90.8 

144.2 

1875 

332.3 

252.3 

280.9 

80.0 

224.9 

158.7 

281.0 

66.0 

14.4 

1876  B 

27.6 

270.8 

49.0 

116.9 

292.8 

73.5 

226.2 

42.1 

246.3 

1877 

82.9 

290.2 

175.8 

152.7 

0.5 

349.4 

169.6 

17.3 

116.6 

1878 

138.1 

309.5 

302.7 

188.6 

68.2 

265.4 

112.9 

352.5 

346.8 

1879 

193.3 

328.9 

69.5 

•      224.4 

135.8 

181.4 

56.3 

327.7 

217.1 

1880  B 

248.7 

347.4 

197.6 

261.3 

203.7 

96.1 

1.4 

303.8 

88.9 

1881 

304.0 

6.8 

324.5 

297.2 

271.4 

12.1 

304.8 

279.0 

319.2 

1882 

359.2 

26.2 

91.3 

333.0 

339.1 

288.0 

248.1 

254.2 

189.4 

1883 

54.4 

45.5 

218.1 

8.9 

46.8 

204.0 

191.5 

229.4 

59.7 

1884  B 

109.8 

64.0 

346.2 

45.8 

114.6 

118.7 

136.7 

205.5 

291.5 

1885 

165.0 

83.4 

113.1 

81.6 

182.3 

34.7 

80.0 

180.7 

161.8 

1886 

220.3 

102.8 

239.9 

117.5 

250.0 

310.7 

23.4 

155.9 

32.0 

1887 

275.5 

122.2 

366.7 

153.3 

317.7 

226.6 

326.7 

131.1 

262.3 

1888  B 

330.9 

140.6 

134.9 

190.2 

25.6 

141.4 

271.9 

107.2 

134.1 

1889 

26.1 

160.0 

261.7 

226.1 

93.2 

57.3 

215.2 

82.4 

4.6 

1890 

81.3 

179.4 

28.5 

261.9 

160.9 

333.3 

158.6 

57.6 

234.6 

1891 

136.6 

198.8 

155.3 

297.8 

228.6 

249.2 

101.9 

32.8 

104.9 

1892  B 

192.0 

217.3 

283.5 

334.7 

296.5 

164.0 

47.1 

8.9 

336.7 

1893 

247.2 

236.6 

50.3 

10.6 

4.2 

79.9 

350.4 

344.1 

207.0 

1894 

302.4 

256.0 

177.1 

46.4 

71.8 

355.9 

293.8 

319.2 

77.2 

1895 

357.6 

275.4 

303.9 

82.2 

139.5 

271.9 

237.1 

294.4 

307.5 

1896  B 

53.0 

293.9 

72.1 

119.2 

207.4 

186.6 

182.3 

270.6 

179.3 

1897 

108.3 

313.3 

198.9 

155.0 

275.1 

102.6 

125.6 

245.7 

49.6 

1898 

163.5 

332.6 

325.7 

190.8 

342.8 

18.5 

69.0 

220.9 

279.8 

1899 

218.7 

352.0 

92.5 

226.7 

50.4 

294.5 

12.4 

196.1 

150.1 

1900  B 

274.1 

10.5 

220.7 

263.6 

118.3    ' 

209.2 

317.5 

172.2 

22.0 

33 


TABLE    III.  —  GmtimutL 

FOH  THE  ARGUMENTS. 

A.    For  the  different  Team.     The  time*  are  referred  to  the  meridian  of  Washington. 

y.  MI 

XXXVII. 

XXXVIII 

XXXIX 

XI. 

XLI. 

XI.  II 

XI.  Ill 

XLIV. 

XLV. 

1852  1! 

'.'17.- 

l-.ui 

0 

1 

o 

in 

0 

161 

o 
103 

O 

10 

0 

214 

O 

63 

]  -:.:) 

1  1  '.'I 

31.1 

m 

m 

147 

146 

128 

8 

l-.VI 

•-•::•.'.'. 

• 

112 

11 

192 

281 

43 

313 

1855 

314.0 

7:I.H 

303 

35 

116 

236 

56 

317 

HI 

MM  G 

216.8 

•J7.VI 

164 

M 

•a 

979 

IM 

233 

903 

1887 

ll-.  •> 

117.4 

M 

213 

325 

m 

HI 

147 

148 

i--.- 

21.0 

318.8 

M 

126 

70 

8 

101 

69 

93 

MM 

•J-i.l 

160.2 

106 

39 

17.-, 

59 

237 

336 

38 

i-i;.i  /; 

1  -.Vl 

2.2 

327 

313 

279 

96 

371 

HI 

344 

i-i,i 

88.0 

',>i»:t.7 

187 

226 

94 

140 

147 

166 

Hi 

i  -<;•.• 

Htt.1 

4.-,.  I 

48 

140 

199 

184 

HI 

81 

233 

i-.;i 

HU 

246.5 

269 

53 

234 

•J 

57 

HI 

178 

M;I  /; 

.    i:.r..o 

88.5 

129 

HI 

339 

M 

192 

271 

194 

1865 

r>7.i 

290.0 

350 

240 

84 

316 

327 

1-:, 

69 

1866 

319.2 

131.4 

211 

153 

188 

1 

102 

100 

14 

1S67 

•--.'I.:! 

332.8 

72 

67 

293 

45 

238 

14 

318 

1868  B 

i-.'l.i 

174.8 

292 

341 

38 

88 

12 

290 

264 

1-.,' 

26.2 

16.3 

153 

254 

143 

133 

148 

204 

209 

1870 

-.'--.•.' 

217.7 

14 

167 

248 

177 

HI 

119 

154 

i-7i 

190.3 

59.2 

235 

80 

352 

221 

58 

33 

99 

1872  B 

93.1 

261.1 

95 

355 

97 

265 

193 

308 

44 

1873 

355.2 

102.6 

316 

968 

202 

309 

328 

223 

349 

1874 

257.3 

304.0 

177 

181 

307 

353 

103 

138 

294 

I-7-. 

139.4 

145.5 

38 

94 

52 

38 

239 

52 

239 

1876  D 

62.2 

347.4 

M 

9 

156 

81 

13 

327 

185 

1877 

324.3 

188.9 

119 

M 

261 

125 

148 

262 

130 

1878 

-j.;.  i 

30.3 

340 

195 

6 

170 

284 

156 

74 

l-7:i 

1-'-.'. 

231.8 

201 

Ml 

111 

214 

59 

71 

19 

1880  B 

31.3 

73.8 

61 

23 

215 

257 

194 

346 

325 

1-1 

293.4 

275.2 

-,'-_' 

296 

320 

M 

329 

261 

270 

I—.' 

1  :>:,.:, 

116.6 

143 

209 

65 

346 

104 

175 

215 

l--:i 

97.6 

318.1 

4 

122 

170 

30 

239 

90 

160 

1884  B 

0.4 

160.1 

224 

37 

274 

74 

14 

5 

105 

1-.-, 

262.5 

1.5 

85 

310 

19 

118 

149 

280 

50 

1886 

164.5 

202.9 

306 

223 

124 

162 

285 

194 

355 

1887 

66.6 

44.4 

166 

136 

229 

207 

60 

109 

HI 

1888  B 

329.4 

306.4 

27 

00 

333 

950 

195 

23 

246 

I--:- 

231.5 

87.8 

248 

•    323 

78 

294 

330 

299 

1!»1 

1-  .,, 

133.6 

HM 

109 

236 

183 

339 

105 

213 

135 

1891 

:r,.7 

130.7 

329 

149 

ne 

S3 

840 

128 

80 

1892  B 

298.5 

332.7 

190 

64 

32 

66 

15 

43 

96 

1893 

200.6 

174.1 

51 

•7 

137 

111 

150 

318 

331 

1894 

102.7 

15.5 

m 

250 

M 

155 

H6 

Hi 

976 

I-'.', 

4.8 

217.0 

132 

163 

347 

199 

61 

147 

991 

1896  B 

267.6 

59.0 

353 

78 

91 

243 

195 

62 

166 

1897 

169.7 

260.4 

214 

Ml 

196 

ma 

331 

336 

111 

1898 

71.8 

101-8 

74 

264 

301 

331 

106 

251 

56 

1899 

333J3 

303.3 

177 

46 

15 

241 

166 

1 

1900  B 

136.7 

145.3 

l.V, 

M 

ISO 

59 

16 

81 

307 

34 


TABLE    III.  —  Continued. 

FOR  THE   ARGUMENTS. 

D.     Variations  of  the  Arguments  for  the  different  Months.     The  times  are  referred  to  the  meridian  of  Washington. 

Months. 

I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 

IX. 

January 

0?000 

o!ooo 

o!ooo 

0.00 

0°00 

0.00 

o°.oo 

o°.oo 

o°.oo 

February 

357.425 

6.209 

1.058 

3.63 

9.85 

21.20 

14.99 

346.07 

348.64 

March 

355.098 

11.817 

2.014 

6.91 

18.74 

40.35 

28.53 

333.48 

338.38 

April 

352.523 

18.026 

3.072 

10.54 

28.59 

61.55 

43.52 

319.55 

327.02 

May 

350.031 

24.035 

4.096 

14.06 

38.12 

82.07 

58.03 

306.07 

316.03 

Jane 

347.456 

30.244 

5.154 

17.69 

47.97 

103.27 

73.02 

292.14 

304.67 

July 

344.964 

36.253 

6.178 

21.21 

57.50 

123.79 

87.53 

278.66 

293.68 

August 

342.389 

42.462 

7.236 

24.84 

67.35 

144.99 

102.52 

264.73 

•  282.32 

September 

339.814 

48.671 

8.294 

28.47 

77.19 

166.19 

117.51 

250.80 

270.96 

October 

337.322 

54.680 

9.318 

31.99 

86.72 

186.71 

132.02 

237.32 

259.97 

November 

334.747 

60.889 

10.376 

35.62 

96.57 

207.91 

147.01 

223.39 

248.61 

December 

332.255 

66.898 

11.400 

39.14 

106.10 

228.43 

161.52 

209.01 

237.62 

Months. 

X. 

XI. 

XII. 

XIII. 

XIV. 

XV. 

XVI. 

XVII. 

XVIII. 

January 

o°.oo 

o°.oo 

o°.oo 

0°00 

o°.oo 

o 

0.0 

o 
0.0 

o 
0.0 

o 
0.0 

February 

358.48 

8.78 

23.78 

16.05 

339.85 

32.6 

343.5 

27.4 

38.8 

March 

357.11 

16.72 

45.26 

30.55 

321.65 

62.0 

328.6 

52.2 

73.8 

April 

355.59 

25.50 

69.04 

46.60 

301.50 

94.6 

312.1 

79.6 

112.6 

May 

354.12 

34.00 

92.05 

62.13 

282.00 

126.1 

296.1 

106.1 

150.1 

June 

352.60 

42.78 

115.83 

78.18 

261.85 

158.7 

279.6 

133.5 

188.9 

July 

351.13 

51.28 

138.84 

93.71 

242.35 

190.2 

263.6 

160.0 

226.4 

August 

349.61 

60.06 

162.62 

109.76 

222.20 

222.8 

247.1 

187.4 

265.2 

September 

348.09 

68.84 

186.39 

125.81 

202.05 

255.3 

230.6 

214.8 

303.9 

October 

346.62 

77.34 

209.40 

141.34 

182.55 

286.8 

214.6 

241.3 

341.4 

November 

345.10 

86.12 

233.18 

157.39 

162.40 

319.4 

198.1 

268.7 

20.2 

December 

343.63 

94.62 

256.19 

172.92 

142.90 

350.9 

182.1 

295.3 

57.7 

Months. 

XIX. 

XX. 

XXI. 

XXII. 

XXIII. 

XXIV. 

XXV. 

XXVI. 

xxvn. 

o 

o 

o 

o 

o 

o 

o 

o 

o 

January 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

February 

8.3 

36.2 

334.7 

350.8 

355.9 

13.5 

328.5 

353.3 

359.5 

March 

15.8 

68.9 

311.9 

342.4 

352.8 

25.6 

300.1 

347.3 

359.1 

April 

24.1 

105.1 

286.6 

333.2 

348.1 

39.1 

268.6 

340.6 

358.6 

May 

32.2 

140.1 

262.1 

324.2 

344.1 

52.2 

238.1 

334.2 

358.2 

June 

40.5 

176.3 

236.8 

315.0 

340.0 

65.6 

206.6 

327.5 

357.7 

July 

48.6 

211.3 

212.3 

306.1 

336.0 

78.7 

176.1 

321.0 

357.3 

August 

56.9 

247.5 

187.0 

296.8 

331.9 

92.1 

144.6 

314.3 

356.8 

September 

65.2 

283.7 

161.7 

287.6 

327.8 

105.6 

113.1 

307.6 

356.3 

October 

73.3 

318.7 

137.2 

278.6 

323.8 

118.6 

82.6 

301.2 

355.9 

November 

81.6 

354.9 

111.9 

269.4 

319.7 

132.1 

51.1 

294.5 

355.4 

December 

89.7 

29.9 

87.4 

260.5 

315.7 

145.2 

20.6 

288.0 

355.0 

In  Bissextile  Years  subtract  one  day  from  the  date  in  the  first  two  months. 

TABLE    III.  —  Continued. 

FOR  THE   ARGUMENTS. 

n.     Variation*  of  the  Arguments  for  the  different  Month*.     The  time*  are  referred  to  the  meridian  of  Washington. 

Monthi. 

XXVI  II 

XXIX 

XXX. 

XXXI. 

XXXII. 

XXX11I 

XXXIV. 

XXXV. 

XXXVI. 

o 

o 

o 

o 

0 

o 

o 

o 

Q 

January 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0X1 

0.0 

0.0 

February 

4.7 

331.1 

41.3 

33.6 

5.7 

322.3 

56.3 

BU 

50.1 

March 

8.9 

ii'H.'i 

78.7 

64.0 

10.9 

IBM 

107.2 

54.2 

95.4 

April 

in.:, 

276.0 

120.0 

97.6 

16.6 

250.6 

163.5 

BU 

n:..:. 

M  ••:• 

18.0 

2»i.O 

160.0 

130.2 

22.2 

214.1 

218.0 

110.2 

194.0 

June 

22.7 

219.1 

201.3 

KM 

27.9 

176.4 

274.4 

au 

244.1 

July 

27.2 

llil.l 

241.3 

196.4 

33.5 

139.9 

HU 

166.2 

2)2.6 

August 

31.8 

1  .,•.'.-.• 

BM 

•_-.:,..,, 

39.2 

102.2 

HJ 

194.6 

342.7 

Septemlicr 

:wi.r, 

133.3 

::•.-.;.' 

KS4 

44.9 

i,l.-, 

814 

223.1 

32.8 

I  triober 

41.0 

105.3 

3.9 

296.2 

50.5 

28.0 

136.1 

MM 

81.3 

Noremlior 

45.6 

194 

45.2 

::-.•  '•- 

56.2 

350.3 

192.4 

279.1 

131.4 

December 

:->.l 

48.4 

B5.2 

2.4 

61-8 

::i:;.- 

246.9 

3C6.6 

179.9 

Monthi. 

XXXVII. 

xxxvin. 

XXXIX. 

XL. 

XLI. 

XI.II. 

X  I.IIl. 

XLIV. 

XLV. 

o 

0 

o 

o 

o 

o 

o 

0 

o 

January 

0.0 

0.0 

0 

0 

0 

0 

0 

0 

0 

February 

22.3 

17.1 

348 

54 

338 

333 

341 

23 

26 

March 

42.4 

32.5 

338 

102 

319 

309 

324 

44 

50 

April 

64.6 

49.6 

326 

156 

297 

282 

305 

67 

76 

May 

86.2 

66.2 

314 

m 

276 

256 

MB 

90 

101 

June 

108.4 

83.3 

303 

262 

•J.-,  1 

229 

267 

113 

127 

July 

130.0 

99.9 

291 

314 

233 

203 

'  248 

136 

152 

August 

152.2 

117.0 

279 

7 

212 

177 

229 

159 

178 

KMlHeiuber 

171.:. 

134.1 

268 

61 

190 

150 

210 

182 

204 

October 

196.0 

150.6 

256 

113 

169 

124 

192 

205 

229 

Norember 

218.3 

167.7 

244 

167 

147 

97 

173 

228 

255 

December 

239.8 

184.3 

333 

219 

126 

71 

154 

250 

260 

In  Bissextile  Years  subtract  one  day  from  the  date  in  the  first  two  months. 

3G 


TABLE    III.  —  Continued. 

FOR  THE  ARGUMENTS. 

C.    Variations  of  the  Arguments  for  the  different  Days.    The  times  are  referred  to  the  meridian  of  Washington. 

Days. 

I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 

IX. 

1 

359?917 

•    0^200 

0?034 

0 

0.12 

0°.32 

0°.68 

o 
0.48 

359°.55 

359°.63 

2 

359.834 

0.401 

0.068 

0.23 

0.64 

1.37 

0.97 

359.10 

359.27 

3 

359.751 

0.601 

0.102 

0.35 

0.95 

2.05 

1.45 

358.65 

358.90 

4 

359.667 

0.801 

0.137 

0.47 

1.27 

2.74 

1.93 

358.20 

358.53 

5 

359.584 

1.001 

0,171 

0.59 

1.59 

3.42 

2.42 

357.75 

358.17 

6 

359.501 

1.202 

0.205 

0.70 

1.90 

4.10 

2.90 

357.30 

357.80 

7 

359.418 

1.402 

0.239 

0.82 

2.22 

4.79 

3.39 

356.85 

357.43 

8 

359.335 

1.602 

0.273 

0.94 

2.54 

5.47 

3.87 

356.40 

357.07 

9 

359.252 

1.803 

0.307 

1.06 

2.86 

6.16 

4.35 

355.95 

356.70 

10 

359.169 

2.003 

0.341 

1.17 

3-18 

6.84 

4.84 

355.51 

356.34 

20 

358.338 

4.006 

0.683 

2.34 

6.35 

13.68 

9.67 

351.01 

352.67 

30 

357.508 

6.009 

1.024 

3.52 

9.53 

20.52 

14.51 

346.52 

849.01 

Days. 

X. 

XI. 

XII. 

XIII. 

XIV. 

XV. 

XVI. 

XVII. 

XVIII. 

1 

359°.95 

o 

0.23 

o 
0.77 

0°52 

359°.35 

o 

1.1 

359°5 

o 
0.9 

o 
1.3 

2 

359.90 

0.57 

1.53 

1.04 

358.70 

2.1 

358.9 

1.8 

2.5 

3 

359.85 

0.85 

2.30 

1.55 

358.05 

3.2 

358.4 

2.7 

3.8 

4 

359.80 

1.13 

3.07 

2.07 

357.40 

4.2 

357.9 

3.5 

5.0 

5 

359.76 

1.42 

3.84 

2.59 

356.75 

5.3 

357.3 

4.4 

6.3 

6 

359.71 

1.70 

4.60 

3.11 

356.10 

6.3 

356.8 

5.3 

7.5 

7 

359.66 

1.98 

5.37 

3.62 

355.45 

7.4 

356.3 

6.2 

8.8 

8 

359.61 

2.27 

6-14 

4.14 

354.80 

8.4 

355.7 

7.1 

10.0 

9 

359.56 

2.55 

6.90 

4.66 

354.15 

9.5 

355.2 

8.0 

11.3 

10 

359.51 

2.83 

7.67 

5.18 

353.50 

10.5 

354.7 

8.8 

12.5 

20 

359.02 

5.67 

15.34 

10.36 

347.00 

21.0 

349.4 

17.7 

25.0 

30 

358.53 

8.50 

23.01 

15.53 

340.50 

31.5 

344.0 

26.5 

37.5 

• 

Days. 

XIX. 

XX. 

XXI. 

XXII. 

XXIII. 

XXIV. 

XXV. 

XXVI. 

xxvn. 

1 

0 

0.3 

o 

1.2 

359^2 

359^7 

359°9 

o 

0.4 

359°0 

359°.8 

o 

0.0 

2 

0.5 

2.3 

358.4 

359.4 

359.7 

0.9 

358.0 

359.6 

0.0 

3 

0.8 

3.5 

357.6 

359.1 

359.6 

1.3 

356.9 

359.4 

0.0 

4 

1.1 

4.7 

356.7 

358.8 

359.5 

1.7 

355.9 

359.1 

359.9 

5 

1.3 

5.8 

355.9 

358.5 

359.3 

2.2 

354.9 

358.9 

359.9 

6 

1.6 

7.0 

355.1 

358.2 

359.2 

2.6 

353.9 

358.7 

359.9 

7 

1.9 

8.2 

354.3 

357.9 

359.1 

3.0 

352.9 

358.5 

359.9 

8 

2.2 

9.3 

353.5 

357.6 

358.9 

3.5 

351.9 

358.3 

359.9 

9 

2.4 

10.5 

352.7 

357.3 

358.8 

3.9 

350.9 

358.1 

359.9 

10 

2.7 

11.7 

351.8 

357.0 

358.7 

4.4 

349.8 

357.9 

359.9 

20 

5.4 

23.4 

343.7 

354.0 

357.4 

8.7 

339.7 

355.7 

359.7 

30 

8.1 

35.0 

335.5 

351.1 

356.0 

13.0 

329.5 

353.6 

359.6 

37 


TABLE    III.—  Continwd. 

FOR  Tin:  AKI.I  MI:  NTS. 

C.    Variations  of  the  Arpuraenu  for  the  different  Duys.     The  time*  are  referred  to  the  meridian  of  Washington. 

XXVIII. 

XXIX 

XXX. 

XXXI 

XXXII. 

XX  XIII. 

X  X  XIV. 

XXXV. 

XXXVI. 

1 

O 

ii.-j 

0 

K0J 

O 

14 

0 

1.1 

o 
0.2 

0 

o 

o 
0.9 

14 

o 

0.3 

:;:.-.! 

2.7 

2.2 

0.4 

3T)7.6 

34 

13 

3.2 

:t 

ii.r, 

VIA 

4.0 

3.3 

0.6 

356.3 

U 

83 

4.9 

4 

ii.  i, 

H6J 

5.3 

4-3 

0.7 

388.1 

7.3 

3.7 

6.5 

5 

03 

IBM 

6.7 

54 

0.9 

9.1 

44 

8.1 

I 

0.9 

354.4 

8.0 

6.5 

1.1 

352.7 

10.9 

54 

9.7 

7 

1.1 

9.3 

74 

1.3 

:i.M.:, 

12.7 

6.4 

11.3 

8 

1..' 

:t-vj.:, 

10.7 

8.7 

1.5 

3.%o.:i 

14.5 

7.3 

12.9 

9 

1.4 

12.0 

9.8 

1.7 

343.0 

16.4 

8.3 

144 

Ml 

1.5 

K0.7 

13.3 

10.9 

1.9 

347.8 

18.2 

9.2 

Hi.-.- 

30 

14 

341.3 

26.7 

21.7 

3.7 

335.7 

36.3 

18.4 

:w.:t 

30 

4.5     i        332-0 

40.0 

:«.r, 

54 

:i23..-, 

:.|..-, 

•.'7.:, 

i-.:, 

Un- 

XXXVII. 

XXXVIII. 

XXXIX. 

XL. 

XLI. 

XLII. 

XI.  Ill 

XLIV. 

XLV. 

o 

0 

0 

O 

0 

0 

o 

o 

1 

0.7 

0.6 

0 

2 

359 

359 

359 

1 

1 

2 

1.4 

1.1 

359 

3 

359 

SBG 

359 

2 

2 

3 

2.2 

1.7 

359 

5 

358 

357 

358 

2 

3 

4 

2-9 

2.2 

359 

7 

357 

357 

:'„-,- 

3 

3 

5 

3.6 

•.'.- 

358 

9 

357 

356 

357 

4 

4 

6 

4.3 

3.3 

358 

10 

356 

KB 

356 

5 

5 

7 

5.0 

3.!) 

357 

12 

355 

354 

356 

5 

6 

8 

5.7 

4.4 

357 

14 

354 

353 

355 

6 

7 

9 

C.5 

5.0 

357 

16 

354 

352 

354 

7 

8 

10 

7.2 

U 

356 

17 

353 

351 

354 

8 

8 

20 

144 

11.0 

352 

35 

346 

343 

MB 

15 

17 

30 

2145 

164 

349 

52 

339 

334 

342 

2! 

25 

38 


TABLE    III.  —  Continued. 

FOR   THE   ARGUMENTS. 

D.     Variations  of  the  Arguments  for  the  different  Hours.     The  times  are  referred  to  the  meridian  of  Washington. 

Hours. 

I. 

II. 

III. 

IV. 

V. 

VI. 

vn. 

VIII. 

IX. 

1 

359.997 

0.008 

o!ooi 

o!oo 

o 
0.01 

0°.03 

0°.02 

359°.98 

359°99 

2 

359.993 

0.017 

0.003 

0.01 

0.03 

0.06 

0.04 

359.96 

359.97 

3 

359.990 

0.025 

0.004 

0.02 

0.04 

0.09 

0.06 

359.94 

359.95 

4 

359.986 

0.033 

0.006 

0.02 

0.05 

0.11 

0.08 

359.92 

359.94 

5 

359.983 

0.042 

0.007 

0.03 

0.07 

0.14 

0.10 

359.90 

359.92 

6 

359.979 

0.050 

0.008 

0.03 

0.08 

0.17 

0.12 

359.89 

359.91 

7 

359.976 

0.058 

0.010 

0.03 

0.09 

0.20 

0.14 

359.87 

359.89 

8 

359.972 

0.066 

0.011 

0.04 

0.11 

0.23 

0.16 

359.85 

359.88 

9 

359.969 

0.075 

0.013 

0.04 

0.12 

0.26 

0.18 

359.83 

359.86 

10 

359.965 

0.083 

0.014 

0.05 

0.13 

0.29 

0.20 

359.81 

359.85 

20 

359.930 

0.166 

0.028 

0.10 

0.26 

0.57 

0.40 

359.62 

359.70 

Hours. 

X. 

XI. 

XII. 

XIII. 

XIV. 

XV. 

XVI. 

XVII. 

XVIII. 

o 

o 

o 

o 

o 

o 

O 

O 

o 

1 

0.00 

0.01 

0.03 

0.02 

359.97 

0.0 

0.0 

0.0 

0.1 

2 

0.00 

0.02 

0.06 

0.04 

359.95 

0.1 

0.0 

0.1 

0.1 

3 

359.99 

0.04 

0.10 

0.07 

359.92 

0.1 

359.9 

0.1 

0.2 

4 

359.99 

0.05 

0.13 

0.09 

359.89 

0.2 

359.9 

0.2 

0.2 

5 

359.99 

0.06 

0.16 

0.11 

359.87 

0.2 

359.9 

0.2 

0.3 

6 

359.99 

0.07 

0.19 

0.13 

359.84 

0.3 

359.9 

0.2 

0.3 

7 

359.99 

0.08 

0.22 

0.15 

359.81 

0.3 

359.9 

0.3 

0.4 

8 

359.98 

0.10 

0.26 

0.17 

359.78 

0.4 

359.8 

0.3 

0.4 

9 

359.98 

0.11 

0.29 

0.20 

359.76 

0.4 

359.8 

0.3 

0.5 

10 

359.98 

0.12 

0.32 

0.22 

359.73 

0.4 

359.8 

0.4 

0.5 

20 

359.96 

0.24 

0.64 

0.24 

359.46 

0.9 

359.6 

0.7 

1.0 

Hours. 

XIX. 

XX. 

XXI. 

XXII. 

XXIII. 

XXIV. 

XXV. 

XXVI. 

XXVII. 

o 

o 

0 

o 

o 

O 

o 

o 

o 

1 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

2 

0.0 

0.1 

359.9 

0.0 

0.0 

0.0 

359.9 

0.0 

0.0 

3 

0.0 

0.2 

359.9 

0.0 

0.0 

0.1 

359.9 

0.0 

0.0 

4 

0.0 

0.2 

359.9 

0.0 

0.0 

0.1 

359.8 

0.0 

0.0 

5 

0.1 

0.2 

359.8 

359.9 

0.0 

0.1 

359.8 

0.0 

0.0 

6 

0.1 

0.3 

359.8 

359.9 

0.0 

0.1 

359.8 

0.0 

0.0 

7 

0.1 

0.3 

359.8 

359.9 

0.0 

0.1 

359.7 

0.0 

0.0 

8 

0.1 

0.4 

359.7 

359.9 

0.0 

0.1 

359.7 

0.0 

.  0.0 

9 

0.1 

0.4 

359.7 

359.9 

0.0 

0.2 

359.6 

.  0.0 

0.0 

10 

0.1 

0.5 

359.7 

359.9 

o.o 

0.2 

359.6 

0.0 

0.0 

20 

0.2 

1.0 

359.3 

359.8 

0.0 

0.4 

359.2 

0.0 

0.0 

39 


TABLE    III.—  Conchil.l. 

FOR  THE   ARGUMENTS. 

D.     Variation*  of  the  Argument*  for  the  different  Hour*.    The  tirae»  arc  referred  to  the  meridian  of  Washington. 

Hour*. 

XXVIII. 

XXIX. 

XXX. 

XXXI 

XXXII. 

xxxni. 

\XXIV. 

XXXV. 

XXXVI. 

0 

0 

o 

o 

o 

o 

o 

o 

p 

1 

0.0 

0.0 

0.1 

0.0 

0.0 

0.1 

0.0 

0.1 

2 

0.0 

IBM 

0.1 

0.1 

0.0 

:ivi.:i 

0.2 

0.1 

0.1 

:t 

0.0 

0.2 

0.1 

0.0 

359.8 

0.2 

0.1 

0.2 

4 

0.0 

0.2 

0.2 

0.0 

359.8 

0.3 

0.2 

0.3 

:. 

0.0 

3894 

0.3 

0.2 

0.0 

3BB.7 

0.4 

0.2 

0.3 

G 

0.0 

:c,<>.- 

0.3 

0.3 

0.1 

359.7 

U 

0.2 

0.4 

7 

0.0 

:r,!  1.7 

0.4 

0.3 

0.1 

:i.-,:u, 

0.5 

0.3 

0.5 

8 

0.0 

my 

0.5 

0.4 

0.1 

BfiM 

0.6 

0.3 

0.5 

:i 

0.0 

3BB.7 

M 

0.4 

0.1 

359.5 

0.7 

0.3 

M 

u 

0.0 

IBM 

0.6 

0.5 

0.1 

359.5 

U 

0.4 

0.7 

90 

0.0 

359.2 

1.1 

0.9 

0.2 

359  J) 

LB 

M 

1.3 

Honrn. 

\\\V1I      XXXVIII. 

XXXIX. 

XL. 

XLI. 

XLII. 

XI.  III. 

XLIV. 

XLV. 

1 

o 
0.0 

o 
0.0 

0 

0 

o 
0 

0 

0 

o 
0 

0 

0 

o 
0 

o 
0 

2 

0.1 

0.1 

0 

0 

0 

0 

0 

0 

0 

3 

0.1 

0.1  - 

0 

0 

0 

0 

0 

0 

0 

4 

(I.I 

0.1 

0 

0 

0 

0 

0 

0 

0 

5 

0.2 

0.1 

0 

0 

0 

0 

0 

0 

0 

6 

0.2 

0.1 

0 

0 

0 

0 

0 

0 

0 

7 

0.2 

0.2 

0 

0 

0 

0 

0 

0 

0 

8 

0.2 

0.2 

0 

1 

0 

0 

0 

0 

0 

9 

0.3 

0.2 

0 

1 

0 

0 

0 

0 

0 

10 

0.3 

0.2 

0 

1 

0 

0 

0 

0 

0 

20 

M 

0.5 

0 

1 

359 

359 

0 

1 

1 

40 


TABLE    IV. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE   SIXTH  DECIMAL. 

Terms  multiplied  with  t.    Argument  =  M. 

Arg. 

Ji 

Diff. 

ft 

Diff. 

Cl 

Diff. 

Arg. 

6 

Diff. 

T!l 

Diff. 

Si 

Diff. 

o 

o 

0 

-    5.24 

-684.22 

-35.71 

45 

+437.82 

-360.75 

+24.69 

1 

+    9.15 

+14-39 

683.87 

+  0-35 

34.59 

+1-12 

46 

440.91 

+3-09 

350.43 

+  10-32 

26.00 

+  1-31 

2 

23.51 

14-36 

683.09 

0-78 

33.45 

1-14 

47 

443.73 

2.82 

340.15 

10-28 

27.29 

1-29 

3 

37.83 

14-32 

681.88 

1-21 

32.29 

1-16 

48 

446.27 

2.54 

329.91 

10-24 

28.57 

1-28 

4 

52.09 

14-26 

680.23 

1.65 

31.11 

1.18 

49 

448.56 

2.29 

319.74 

10-17 

29.84 

1-27 

5 

66.27 

14-18 

678.17 

2-06 

29.91 

1-20 

50 

450.58 

2.02 

309.63 

10-11 

31.10 

1-26 

6 

80.37 

14-10 

675.69 

3*48 

28.69 

1-22 

51 

452.36 

1.78 

299.58 

10-05 

32.34 

1-24 

7 

94.35 

13-98 

672.80 

3-89 

27.45 

1-24 

52 

453.88 

1.53 

289.61 

9-97 

33.57 

1-23 

8 

108.20 

13.85 

669.51 

3-29 

26.19 

1-26 

53 

455.17 

1.Q9 

279.72 

9-89 

34.79 

1-22 

9 

121.91 

13-71 

665.82 

3-69 

24.92 

1-27 

54 

456.22 

1-05 

269.90 

9-82 

35.99 

1.20 

13-56 

4-09 

1.29 

0-82 

9-73 

1-18 

10 

+135.47 

-661.73 

-23.63 

55 

+457.04 

-260.17 

+37.17 

11 

148.84 

+13-37 

657.27 

+  +.46 

22.33 

+1-30 

56 

457.64 

+0-60 

250.53 

+  9.64 

38.34 

+1-17 

12 

162.03 

13-19 

652.42 

4-S5 

21.01 

1-32 

57 

458.02 

0-38 

240.98 

9.55 

39.50 

1-16 

13 

175.01 

112-98 

647.19 

5-23 

19.68 

1.33 

58 

458.19 

+0-17 

231  .53 

9-45 

40.64 

1.14 

14 

187.77 

12-76 

641.62 

6-57 

18.34 

1-34 

59 

458.16 

-0-03 

222.18 

9.35 

41.77 

1-13 

15 

280.31 

lfc.54 

635.69 

6-93 

.   16.99 

1.35 

60 

457.94 

0-22 

212.93 

9-25 

42.88 

1-11 

16 

212.60 

12-29 

629.42 

6-27 

15.63 

1-36 

61. 

457.53 

0-41 

203.79 

9.14 

43.97 

1-09 

17 

224.65 

12-05 

622.84 

6-68 

14.25 

1.38 

62 

456.94 

0-59 

194.75 

9-04 

45.05 

1-08 

18 

236.45 

11-80 

615.94 

6-90 

12.87 

1-38 

63 

456.17 

0-77 

185.82 

8-93 

46.11 

1-06 

19 

247.98 

11-53 

608.74 

7-20 

11.48 

1*39 

64 

455.23 

0-94 

177.01 

8.81 

47.15 

1-04 

11.24 

7-48 

1-39 

1-11 

8-70 

1-03 

20 

+259.22 

-601.26 

-10.09 

65 

+454.12 

-168.31 

+48.18 

21 

270.19 

+10-97 

593.51 

+  7-78 

8.69 

+1-40 

66 

452.85 

-1-27 

159.72 

+  8.59 

49.19 

+  1-01 

22 

280.86 

10-67 

585.50 

8-01 

7.28 

1-41 

67 

451.42 

1.43 

151.25 

8-47 

50.18 

0-99 

23 

291.23 

10-37 

577.25 

8-25 

5.87 

1-41 

68 

449.84 

1.58 

142.89 

8-3G 

51.16 

0-98 

24 

301.29 

10-06 

568.77 

8-48 

4.45 

1-42 

69 

448.12 

1-72 

134.65 

8-24 

52.12 

0-96 

25 

311.04 

9-75 

560.07 

8-70 

3.03 

1-42 

70 

446.26 

1-86 

126.53 

8-12 

53.06 

0-94 

26 

320.46 

9.42 

551.17 

8-90 

1.61 

1-42 

71 

444.26 

2-00 

118.54 

7-99 

53.98 

0-92 

27 

329.56 

9-10 

542.08 

9-09 

-  0.19 

1-42 

72 

442.13 

2-13 

110.66 

7-88 

54.89 

0-91 

28 

3^8.32 

8-76 

532.81 

9.27 

+  1.23 

1-42 

73 

439.88 

2-25 

102.91 

7-75 

55.78 

0-89 

29 

346.74 

8-42 

523.39 

9-42 

2.65 

1-42 

74 

437.51 

2-37 

95.28 

7-63 

56.65 

0-87 

8-09 

9.58 

1-42 

2-49 

7-51 

0*85 

30 

354.83 

-513.81 

+  4.07 

75 

+435.02 

-  87.77 

+57.50 

31 

+362.62 

+  7-79 

504.09 

+  9-72 

5.48 

+1-41 

76 

432.42 

-2-60 

80.39 

+  7-38 

58.33 

+0-83 

32 

370.07 

7-45 

494.25 

9-84 

6.90 

1-42 

77 

429.72 

2-70 

73.12 

7-27 

59.15 

0-82 

33 

377.21 

7-14 

484.30 

9-95 

8.31 

1-41 

78 

426.92 

2.80 

65.98 

7-14 

59.94 

0-79 

34 

384.01 

6-80 

474.25 

10-05 

9.71 

1-40 

79 

424.02 

2-90 

58.96 

7-02 

60.72 

0-73 

35 

390.48 

6.47 

464.12 

10-13 

11.11 

1-40 

80 

421.02 

3-00 

52.07 

6-89 

61.48 

0-76 

36 

396.63 

6-15 

453.91 

10-21 

12.51 

1-40 

81 

417.93 

3-09 

45.29 

6.78 

62.23 

0-75 

37 

402.45 

5.82 

443.65 

10.28 

13.89 

1-38 

82 

414.76 

3-17 

38.64 

6-65 

62.95 

0-72 

38 

407.95 

6-50 

433.35 

10-30 

15.27 

1-38 

83 

411.50 

3-26 

32.10 

6.54 

63.66 

0-71 

39 

413.13 

5-18 

423.01 

10-34 

16.65 

1-38 

84 

408.17 

3.33 

25.68 

6-42 

64.35 

0-69 

4.87 

10-36 

1.36 

3-41 

6.30 

0-67 

40 

+418.00 

-412.65 

+18.01 

85 

+404.76 

-  19.38 

+65.02 

41 

422.57 

+  4-57 

402.27 

+10-38 

19.37 

+1.36 

86 

401.29 

-3-47 

13.20 

+  6-18 

65.67 

+0-68 

42 

426.82 

4-25 

391.88 

10-39 

20.72 

1*35 

87 

397.75 

3*54 

7.13 

6-07 

66.30 

0-63 

43 

430.78 

3-96 

381.49 

10-39 

22.05 

1-33 

88 

394.14 

3.61 

1.18 

5.95 

66.92 

0-62 

44 

434.45 

3-67 

371.11 

10-38 

23.38 

1-33 

89 

390.47 

3-67 

+    4.66 

5-84 

67.51 

0-59 

45 

+437.82 

+  3-37 

-360.75 

+10-36 

+24.69 

+1-31 

90 

+386.75 

-3.72 

+  10.39 

+  5-73 

+68.09 

+0-68 

II 


TABLE    IV.—  Cunt, 

I'KUTI  lil'.ATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

Terms  multiplied  with  (.    Argument  =  M. 

Ar* 

5, 

Diff. 

1l 

Diff. 

,& 

Diff. 

Ji 

Diff. 

Th 

Diff. 

f, 

Diff. 

0 

0 

90 

»-  H).:P.I 

+68.09 

m 

+173.00 

+76.34 

:>1 

-»-T8 

II..IHI 

+5.61 

+o.&« 

136 

188.14 

-4-47 

174.96 

+I.M 

76.16 

-0-18 

'.'•.' 

:i7'.i.i4 

S.«3 

•-M..-.I 

6.41 

8MO 

0.46 

137 

183.66 

4*48 

i7i;.-»i 

1*90 

T:,/I, 

0.90 

n 

37MI 

J.8H 

4-39 

0.41 

138 

179.18 

4-47 

178.70 

1-84 

75.75 

O-'Jl 

M 

:i7i.:« 

3-93 

B.19 

4-39 

nx 

0-40 

174.72 

4-47 

l-ii.in 

1«W 

75JJ3 

o-w 

B6 

:«;:.:i7 

3.98 

:i7.:t7 

4-18 

70.71 

0-48 

140 

170.25 

4-47 

182.23 

1-74 

75.29 

0-94 

96 

:ui:t.:«i 

4-01 

i-.1.  i:. 

4.08 

71.1- 

0.47 

141 

h,,.T- 

4-47 

18*41 

149 

75.03 

0--M 

\<7 

S69JO 

4  -04 

17.  l:l 

4-98 

7l.t,.i 

0-49 

142 

161.32 

4-46 

185.56 

1-M 

74.77 

0-98 

;j.V).-zt 

Ml 

B&90 

4-87 

72.07 

0.44 

143 

1.VJ.87 

4-44 

187.14 

1-46 

74.49 

0-98 

M 

::.,l.n 

t-i-j 

:,7.o7 

4-T7 

0.43 

144 

1  .VJ.M 

4-4« 

188.68 

1-44 

74.20 

0-39 

4-U 

4.«T 

0-40 

4-44 

l-4» 

0-31 

100 

H346JK 

+  61.74 

+72.89 

145 

+147.% 

+  i:Mi.i7 

+73.69 

Ml 

-4-18 

66.32 

+4.18 

73.27 

+0-38 

146 

143..VJ 

-4-44 

Ml.i.l 

+144 

73.57 

-0-39 

UN 

4-JO 

70.79 

4'4T 

73.63 

0-M 

147 

139.07 

'    4.44 

193.00 

•39 

73.24 

0-33 

108 

334.36 

4*31 

7.-..1- 

4-39 

73.98 

0.34 

148 

134.64 

4.43 

194.34 

•34 

72.S9 

0-34 

104 

330.09 

4-M 

7'  Mi, 

4-28 

74.31 

0-3* 

140 

130.20 

4-44 

I'.u.i.l 

•30 

72.53 

0-36 

105 

4-98 

83.66 

4.90 

74.62 

0-31 

150 

lv>:,.77 

4-43 

HKi.'.MI 

•98 

72.16 

0-37 

106 

3-JI..-.I 

4-80 

87.76 

4-10 

74.92 

0-30 

151 

121.34 

403 

196.11 

•31 

71.77 

0-39 

107 

317.19 

4-3J 

91.78 

4411 

75.l:i 

0-97 

152 

in,,  -j 

4.43 

199.28 

•17 

71.38 

0-39 

108 

312.85 

4-34 

95.70 

3.93 

1MB 

0-tt 

153 

112.50 

I-I-J 

200.40 

•19 

70.97 

0-41 

109 

n&ao 

4-34 

99.54 

3.84 

75.70 

0-'J4 

154 

108.08 

4-43 

201.48 

140 

70^4 

0-43 

4-37 

3-76 

0.33 

l-ll 

1-04 

0-43 

110 

+304.13 

+103.30 

l.V, 

+103.67 

+202.52 

+70.11 

111 

-4-38 

106.97 

+».«7 

76.13 

+0.31 

156 

90.26 

-4-41 

203.52 

+  1-00 

69.66 

-0-44 

II.' 

4-40 

II"..-,.-, 

3.48 

76.32 

0-19 

157 

94.85 

441 

204.48 

0-98 

60.20 

0*48 

111! 

4-41 

114.06 

3.41 

76.50 

0-18 

158 

90.45 

4-40 

20.-..40 

0-99 

68.73 

0-17 

114 

286.52 

4.4-] 

117.4* 

3-49 

76.66 

0-16 

159 

86.05 

4-40 

206.28 

0-88 

68.25 

0-48 

US 

M&68 

4-4* 

120.83 

3-34 

7ii.-.i 

0-14 

160 

81.65 

4*40 

207.12 

0-84 

67.75 

0-40 

116 

277.66 

4.4* 

124.10 

3-37 

7i;.":i 

0-13 

161 

77.25 

4-40 

207.92 

0-80 

67.24 

0-41 

117 

273.21 

4-44 

127.29 

3-19 

77.04 

0-11 

162 

72.86 

4.39 

208.68 

0-76 

66.72 

0-49 

118 

4-44 

130.41 

3.13 

77.13 

0-09 

163 

68.47 

4-89 

809.40' 

0-79 

66.19 

0-43 

ll'.i 

264.30 

4.46 

133.45 

3-04 

77.21 

0-08 

164 

64.08 

4-39 

210.09 

0.«9 

65.65 

0-M 

4-Hi 

M7 

0-0« 

I..TO 

0-68 

0.44 

130 

+259.84 

+136.42 

+77.27 

165 

+  59.69 

+210.74 

+65.10 

!    121 

-4-47 

139.32 

+•1.90 

77.32 

+0-0» 

166 

55.30 

-4-39 

211.35 

+0-«1 

64.54 

-o.»« 

i  •-••-• 

-.•:.  >.-  • 

4.48 

142.14 

9.82 

77.35 

0-03 

167 

50.92 

4*38 

211.!I2 

0-»7 

63.96 

0-68 

123 

•J|.,.rj 

•I-  IT 

144.90 

8-76 

77.36 

+0-01 

168 

4MB 

4*39 

2)2.46 

0-44 

63.37 

0-59 

124 

241.94 

4-48 

147.60 

S-70 

77.36 

0-00 

169 

42.15 

4-38 

212.96 

0-40 

62.78 

0-49 

198 

4-18 

I60J9 

a.«i 

77.34 

-0-09 

170 

37.77 

4-38 

213.42 

0-46 

62.17 

0-81 

196 

•j  :•_'.  ••; 

4-49 

158.76 

3-M 

77.31 

0-0$ 

171 

33.38 

4.39 

2IH.K-, 

0-43 

61.55 

127 

UM0 

4-48 

15M7 

»-49 

77.26 

0-06 

172 

29.00 

4.38 

214.24 

0-39 

60.02 

0-63 

123 

SMI 

4.49 

157.70 

9.4* 

77.20 

0-08 

173 

24.62 

4*38 

-Jll.V. 

r.34 

60.29 

0-83 

129 

21931 

4.49 

160.07 

2-17 

77.12 

0*08 

174 

20.23 

4-39 

2)4.91 

0-39 

.Vi..,! 

0-S4 

4-48 

I'M 

0-09 

4-38 

0-99 

O.M 

130 

.•.•[.-..in 

+162.37 

+77.03 

175 

+  15.65 

+2I5J20 

.:.-.•- 

131 

•-'M..-.4 

-4-49 

164.62 

+J.S* 

76.92 

-0.11 

176 

11.46 

-4-39 

215.44 

+0^4 

:.-.::  l 

-047 

132 

206.06 

4-48 

166.80 

9.18 

TfcfiQ 

0-19 

177 

7.08 

4.38 

215.65 

0.91 

57.63 

0-88 

133 

201.58 

4-4H 

168.92 

I'll 

76.66 

0-14 

178 

+    269 

4-39 

215.82 

0-17 

56.95 

0-88 

134 

107.00 

4-49 

170.09 

3-07 

7i,.:,l 

0-16 

179 

-    1.70 

4-39 

215.96 

0-14 

56.25 

0-70 

138 

+192.61 

-4-48 

+173.00 

+9*1 

1-76.34 

-0-17 

180 

-    6.09 

-4-39 

+216.06 

+0-10 

+55.54 

-0-71 

42 


TABLE    IV.  —  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

Terms  multiplied  with  t.    Argument  =  M. 

Arg. 

li 

Diff. 

«h 

Diff. 

& 

Diff. 

Arg. 

Si 

Diff. 

»h 

Diff. 

£1 

Diff. 

o 

o 

180 

-     6.09 

+216.06 

+55.54 

225 

-208.16 

+178.25 

+15.94 

181 

10.48 

-4-39 

216.12 

+0-06 

54.82 

-0-73 

226 

212.78 

-4-62 

176.30 

—1-95 

14.94 

-1-00 

182 

14.88 

4-40 

216.15 

+0-03 

54.10 

0-72 

227 

217.40 

4-62 

174.29 

2.01 

13.94 

1-00 

183 

19.27 

4-39 

216.13 

-0-03 

53.36 

0-74 

228 

222.02 

4-62 

172.23 

2-06 

12.93 

1-01 

134 

23.67 

4.40 

216.09 

0-04 

52.62 

0.74 

229 

226.64 

4-62 

170.11 

2.12 

11.92 

1-01 

185 

28.07 

4.40 

216.00 

0-09 

51.86 

0-76 

230 

231.27 

4-63 

167.92 

2-19 

10.91 

1-01 

186 

32.48 

.4-41 

215.88 

0-12 

51.10 

0-76 

231 

235.90 

4-63 

1G5.68 

2  24 

9.90 

1.01 

187 

36.88 

4-40 

215.72 

0-16 

50.33 

0-77 

232 

240.53 

4-63 

163.37 

2.31 

8.88 

1  02 

188 

41.29 

4-41 

215.52 

0-30 

49.55 

0-78 

233 

245.16 

4-63 

160.99 

2-38 

7.86 

1-02 

189 

45.71 

4-43 

215.29 

0-33 

48.77 

0-78 

234 

249.79 

4-63 

158.55 

2-46 

6.84 

1-02 

4-42 

0-27 

0-80 

4.03 

2-51 

1-02 

190 

-  50.13 

+215.02 

+47.97 

235 

-254.42 

+156.04 

+  5.82 

191 

54.55 

-4-42 

214.71 

-0-31 

47.17 

-0-80 

236 

259.05 

-4-63 

153.46 

-2-68 

4.80 

-1  02 

192 

58.97 

4-43 

214.37 

0-34 

46.36 

0  81 

237 

263.67 

4-62 

150.80 

2  66 

3.78 

1  02 

193 

63.40 

4-43 

213.99 

0-38 

45.54 

0-82 

238 

268.30 

4-63 

148.08 

2-72 

2.76 

1-02 

194 

67.84 

4.44 

213.57 

0-42 

44.71 

0-83 

239 

272.92 

4-62 

145.28 

2-tO 

1.73 

1.03 

195 

72.28 

4.44 

213.11 

C-16 

43.87 

0  84 

240 

277.54 

4-63 

142.40 

2-88 

+  0.71 

1  02 

196 

76.72 

4-44 

212.61 

0.50 

43.03 

0-84 

241 

282.16 

4-62 

139.44 

2-96 

-  0.31 

1  02 

197 

81.17 

4-45 

212.07 

0-54 

42.18 

0.85 

242 

286.77 

4-61 

136.40 

3  04 

1.34 

1.03 

198 

85.63 

4-46 

211.49 

0-58 

41.32 

o-ee 

243 

291.37 

4-60 

133.28 

3-12 

2.36 

1-02 

199 

90.09 

4.46 

210.87 

0-G2 

40.46 

0-86 

244 

295.96 

4-59 

130.08 

3-CO 

3.39 

1-03 

4-46 

0-67 

0-87 

4-59 

3.28 

1-02 

200 

-  94.55 

+210.20 

+39.59 

245 

-300.55 

+126.80 

-  4.41 

201 

99.02 

-4-47 

209.50 

-0-70 

38.71 

-0-88 

246 

305.13 

-4-58 

123.44 

-3.36 

5.43 

-1  02 

202 

103.50 

4.48 

208.75 

0-75 

37.82 

0-89 

247 

309.70 

4-57 

119.99 

3.45 

6.45 

1-02 

203 

107.98 

4.46 

207.95 

0-80 

36.93 

0-89 

248 

314.25 

4*55 

116.45 

3.54 

7.47 

1-02 

204 

112.47 

4-49 

207.10 

0*85 

36.03 

0-90 

249 

318.79 

4-54 

112.83 

3  62 

8.49 

1-02 

205 

116.97 

4-50 

206.21 

0-89 

35.13 

0-90 

250 

323.32 

4.53 

109.12 

8.71 

9.51 

1  02 

206 

121.47 

4*50 

205.28 

0-93 

34.22 

0-91 

251 

327.83 

4-51 

105.32 

S  80 

10.52 

1-01 

207 

125.98 

4-51 

204.30 

0-99 

33.30 

0-92 

252 

332.33 

4-50 

101.43 

3.89 

11.53 

1-01 

208 

130.49 

4-51 

203.28 

1-02 

32.38 

0-92 

253 

336.81 

4-48 

97.45 

3-93 

12.54 

1  01 

209 

135.01 

4.53 

202.20 

1-08 

31.45 

0-93 

254 

341.27 

4.46 

93.38 

4-07 

13.55 

1  01 

4-53 

1-12 

0-93 

4*44 

4-16 

i  no 

210 

-139.54 

+201.08 

+30.52 

255 

-345.71 

+  89.22 

-14.55 

211 

144.07 

-4-53 

199.91 

-1-17 

29.58 

-0-94 

2T>6 

350.12 

-4-41 

84.96 

-4-26 

15.55 

-1.00 

213 

148.61 

4.54 

198.70 

1-21 

28.63 

0*95 

257 

354.51 

4-39 

80.60 

4-36 

16.54 

0-99 

213 

153.16 

4-55 

197.43 

1-27 

27.68 

0.95 

258 

358.88 

4-37 

76.14 

4-46 

17.54 

LOO 

214 

157.71 

4-55 

196.12 

1.31 

26.73 

0-95 

259 

363.21 

4-33 

71.58 

4-56 

18.52 

0.98 

215 

162.27 

4-56 

194.75 

1.37 

25.77 

0-96 

260 

367.51 

4-30 

66.92 

4-66 

19.51 

0-99 

216 

166.83 

4*56 

193.34 

1-41 

24.81 

0.90 

261 

371.79 

4-38 

62.16 

4-76 

20.49 

0-98 

217 

171.41 

4.58 

191.87 

1-47 

23.84 

0>97 

262 

376.03 

4.34 

57.29 

4-87 

21.46 

0-97 

218 

175.98 

4-87 

190.35 

>    1.S2 

22.87 

0-97 

263 

380.23 

4-20 

52.32 

4-97 

22.43 

0-97 

219 

180.56 

4.58 

188.79 

1-56 

21.89 

0-98 

264 

384.39 

4-16 

47.24 

5-08 

23.39 

0-% 

4.89 

1.03 

0  98 

4-13 

6.19 

0-96 

220 

-185.15 

+187.16 

+20.91 

265 

-388.51 

+  42.05 

-24.35 

221 

189.74 

—4-59 

185.49 

-1-67 

19.92 

-0-99 

266 

392.59 

-4-08 

36.75 

-5.30 

25.30 

-0.95 

222 

194.34 

4-60 

183.76 

1-73 

18.93 

0-99 

267 

396.62 

4-03 

31.34 

5-41 

26.24 

0-94 

223 

198.94 

4-60 

181.98 

1-78 

17.94 

0-99 

268 

400.60 

3.98 

25.82 

6-52 

27.18 

0-94 

224 

203.55 

4*61 

180.14 

1-84 

16.94 

1-00 

269 

404.53 

3-93 

20.18 

6-64 

28.11 

0-93 

225 

-208.16 

—4-61 

+178.25 

-1.89 

+15.94 

-1-00 

270 

-408.40 

—3-87 

+  14.43 

-6-76 

-29.03 

-0-92 

43 


~1 

TABLE    IV.—  Cmitimud. 
I'KIHTKIi.VTIOXS  OF  TIIK  CO-ORDIXATKS  IN   I  NITS  OF  TIIK   SIXTH   DECIMAL. 
Terrai  multiplied  with  I.    Argument  —  if. 

Si 

HiiV. 

1l 

Diff. 

& 

Diff. 

Arg. 

«l 

Diff. 

',: 

Diff. 

tl 

Diff. 

o 

o 

•-Til 

•    14.43 

-29.03 

us 

-457.24 

-365  J2 

-56.92 

-.Tl 

out 

-1-81 

MB 

-  5-87 

•_•>.:>:, 

-0.93 

316 

+  1.W 

375.78 

-HM6 

57.09 

-0.17 

•-•:•.' 

ll&M 

1.76 

S-99 

0.91 

at) 

44'.l.75 

3-90 

386.26 

10-48 

57.23 

0-14 

03 

IT'...:, 

M| 

I1..M 

t.-ll 

31.76 

0-90 

:-.!- 

445.57 

4*18 

::•(,.::. 

10.49 

57.35 

0-13 

tn 

••  : 

9.77 

6.73 

M4B 

.-, 

319 

441.07 

4-M 

407.22 

10.47 

57.44 

009 

I-.-  ..-.' 

1-M 

16.11 

604 

:u.:,:i 

0.88 

BH 

436.26 

4*81 

417.67 

10-45 

5750 

0-06 

1-47 

•-".'.:.- 

6-47 

34.40 

0-87 

321 

431.15 

.-••11 

mm 

10-43 

57.54 

0-04 

an 

433.68 

•j'.l- 

MO 

35.26 

0.88 

322 

6.44 

438.48 

10-19 

57.55 

-0-01 

436.'.» 

LSI 

::.-..-• 

Ml 

KJI 

0-86 

323 

419.95 

6.76 

44-.-J 

10-14 

r.7.:.:t 

+0-03 

•::  ' 

4IH.-JI 

..-: 

42.73 

6.84 

36.96 

0-84 

324 

413^7 

8-08 

459.11 

10-19 

67.48 

0-0* 

1-1.1 

6.M 

0-83 

6-41 

10-31 

0-08 

BM 

-37.79 

M 

-407.46 

-469.34 

-57.40 

•--i 

446.38 

-144 

HJG 

-  7^» 

::-.i.  1 

MB 

400.72 

+  8-74 

479.48 

-10-14 

:.7.-.-,' 

+0-11 

M 

3-94 

6U0 

7-11 

39.41 

O-t-0 

327 

3JI3.66 

7-06 

-l-'.:,:i 

1005 

B7.J5 

0-14 

M 

168.18 

9.8) 

744 

40.21 

0-80 

328 

HM| 

7-40 

499.48 

9-M 

56.98 

0-17 

•-•-I 

2-73 

7-.-<> 

7-47 

40.!»!l 

0-78 

329 

mju 

7-71 

509.30 

9-83 

56.78 

C-30 

•->-. 

2-82 

BUB 

7-» 

41.76 

0-77 

330 

370.4H 

519.00 

9-70 

5655 

0*31 

M 

3.49 

94.10 

7.71 

tut 

0-76 

331 

362.10 

-   •.. 

.v,'-.:,i 

9-M 

56.2!l 

O.M 

M 

462.36 

3.18 

101.94 

7.84 

43.26 

0-74 

M 

ai:t.:Ki 

8-71 

537.91 

9-17 

56.00 

0-39 

..... 

!•.!.'.' 

0.34 

101».90 

7.M 

43.W 

0.71 

333 

344.36 

9.01 

547.12 

9*31 

sue 

0-13 

M 

466.72 

•Ml 

117.!C.l 

..,,, 

44.71 

0-75 

334 

335.01 

B-3S 

556.14 

9*03 

55.33 

0-35 

1-M 

8--J1 

0-70 

9-G7 

8.81 

0-18 

290 

-468.70 

-126.20 

-45.41 

335 

-325.34 

5M4B 

•_"i 

47n-.il 

-1-84 

-  8-U 

46.10 

336 

3i.i.:v. 

+  9-90 

B7U6 

-  8.61 

54.54 

+0-41 

ITJ.-J: 

1.69 

II-.'.- 

8.4ft 

46.77 

0-«7 

337 

:«>r,.ii:i 

10-3-J 

KIM 

en 

54.10 

"•II 

293 

47:f.7(J 

1.&3 

1.11.  .1.1 

8.57 

IT.U 

0-6S 

338 

294.42 

1041 

590.06 

8-U 

53.62 

0-48 

ZM 

47."..  11 

|.«8 

160.24 

48.06 

064 

339 

2K1.51 

10-91 

597.95 

7-89 

r.:f.i-.> 

0-10 

M 

476.36 

1-M 

169.05 

8.81 

48.66 

O.M 

340 

272.30 

11--J1 

605.56 

7-61 

sue 

0-64 

296 

477.40 

144 

177.97 

B.M 

49.23 

0.61 

341 

269.82 

11-48 

612.89 

7-11 

52.01 

0-57 

47-.-J7 

0-87 

187.01 

•'•"1 

49.87 

0-«8 

342 

249.07 

11-75 

<;io.'.i3 

7-04 

51.42 

0-59 

M 

478.96 

0-89 

I'M.  .11. 

*•!« 

50.44 

0-S7 

343 

237.06 

1Q-01 

626^6 

6-71 

50.79 

0.61 

M 

479.46 

0.90 

205.42 

••M 

50.99 

0-U 

344 

224.81 

!•.'•« 

.,:;:;.ri. 

8-40 

50.13 

0-86 

0-33 

9-M 

0-tl 

IJ-40 

049 

300 

-479.78 

-214.78 

-51.12 

345 

-212.31 

-639.14 

-49.44 

Hill 

479.00 

-0-13 

224.2T, 

-  »-47 

.v.'.n:; 

-0-»1 

346 

UM9 

-I-U-7H 

644.88 

-  5-74 

48.72 

+O.TS 

302 

47*81 

-H).09 

-.'.•.::.-.' 

».57 

ma 

0-49 

347 

186.65 

13-94 

6S046 

6-18 

47.97 

0.75 

47'.t.VJ 

0-29 

•J  1:1.4- 

9.86 

0-47 

348 

I7:!..m 

13-15 

85UB 

6-03 

47.19 

0-78 

304 

479.00 

0-53 

»-76 

53.44 

0-4S 

349 

160.15 

13-U 

6B0JH 

4-61 

46.39 

0-90 

305 

•17-.  -.-7 

0.7* 

263.09 

9.8* 

53^7 

0-43 

350 

146.64 

13-61 

664.16 

4*35 

4.-...V, 

0-84 

306 

477.30 

0.«7 

273.02 

9-ra 

54.28 

0-41 

an 

M..  . 

668.09 

1-86 

44.69 

0-86 

307 

476.10 

I'M 

10-00 

54.67 

0-39 

352 

119.11 

13-84 

671.48 

1-48 

43.79 

0-90 

M 

474.65 

1-45 

293.10 

10-08 

65.03 

0-38 

3.13 

105.16 

13-95 

674.13 

1-OJ 

42.87 

0-91 

309 

472.06 

149 

303.26 

10-18 

65.37 

0-34 

3.14 

91.08 

:;..  - 

677.18 

2-«5 

41.93 

0-94 

1-M 

io.» 

0-34 

11.17 

3.34 

0-98 

310 

-471.01 

-31.1.48 

a.Vi 

-  76.91 

-679.42 

-40.95 

311 

46-1.79 

+3.» 

Sil.Tr. 

-lo-r: 

-0-10 

aie 

i  .•.'.«  ,7 

+14-14 

681.24 

-  1-83 

:v.t.'.ir. 

+1-00    1 

312 

466.32 

3-47 

334.08 

10.33 

56.26 

0-77 

a-,7 

048 

11.31 

682.63 

1  39 

:\<M 

1-03    1 

313 

463.17 

».7» 

344.46 

10-18 

56.50 

O..M 

34.01 

11-35 

6S3.60 

0-97 

:::.-- 

141    1 

314 

46n..v. 

S-03 

354.88 

10-43 

66.72 

0-M 

3.19 

19.63 

1!.     - 

684.19 

0-93 

36.81 

147    1 

315 

-457.24 

+  3.31 

-365.32 

-10-44 

-fi6.!>2 

-o-» 

360 

-    5.24 

•  ;  i-;. 

-6-4.22    -0"0 

-M.71 

-H-10    1 

44 


TABLE    IV.—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  I. 

Arg. 

Si 

Diff. 

% 

Diff. 

tl 

Diff. 

Arg. 

fi 

Diff. 

ft 

Diff. 

& 

Diff. 

0 

o 

0 

-577 

4177 

421 

45 

4  303 

4928 

437 

1 

570 

4  7 

201 

424 

21 

0 

46 

339 

436 

933 

4  5 

38 

41 

2 

562 

8 

225 

24 

21 

0 

47 

375 

36 

936 

3 

38 

0 

3 

554 

8 

248 

23 

22 

+1 

48 

412 

37 

938 

2 

39 

1 

4 

545 

9 

271 

23 

22 

0 

49 

450 

38 

940 

4  2 

40 

1 

Q 

23 

Q 

38 

1 

5 

536 

294 

22 

50 

488 

939 

41 

1 

6 

526 

10 

316 

22 

22 

0 

51 

527 

39 

938 

1 

41 

0 

JJ 

'*'' 

1 

40 

3 

7 

515 

338 

23 

52 

567 

935 

42 

1 

8 

504 

11 

360 

22 

23 

0 

53 

607 

40 

930 

5 

43 

1 

9 

493 

11 

381 

21 

23 

0 

54 

648 

41 

925 

5 

44 

1 

12 

21 

0 

41 

8 

1 

10 

-481 

4402 

423 

55 

4  689 

4917 

445 

11 

468 

413 

423 

421 

24 

41 

56 

731 

442 

908 

-  9 

46 

41 

12 

455 

13 

444 

21 

24 

0 

57 

773 

42 

898 

10 

46 

0 

13 

441 

14 

464 

20 

24 

0 

58 

815 

42 

885 

13 

47 

1 

14 

427 

14 

484 

20 

24 

0 

59 

857 

42 

871 

14 

48 

1 

15 

413 

14 

503 

19 

24 

0 

60 

900 

43 

856 

15 

49 

1 

16 

398 

15 

522 

19 

25 

1 

61 

942 

42 

838 

18 

50 

1 

17 

383 

15 

542 

20 

25 

0 

62 

985 

43 

819 

19 

50 

0 

18 

367 

16 

560 

18 

25 

0 

63 

1027 

42 

798 

21 

51 

1 

19 

350 

17 

579 

19 

25 

0 

64 

1069 

42 

775 

23 

51 

0 

17 

18 

1 

42 

25 

1 

20 

-333 

4597 

426 

65 

41111 

4750 

452 

21 

316 

417 

615 

418 

26 

40 

66 

1153 

442 

723 

-27 

52 

4o 

22 

298 

18 

633 

18 

26 

d 

67 

1194 

41 

695 

38 

53 

1 

23 

279 

19 

650 

17 

26 

0 

68 

1234 

40 

665 

30 

53 

0 

24 

260 

19 

667 

17 

27 

1 

69 

1274 

40 

632 

?3 

54 

4i 

25 

241 

19 

684 

17 

27 

0 

70 

1314 

40 

598 

34 

54 

0 

26 

220 

21 

701 

17 

27 

0 

71 

1352 

38 

•563 

35 

54 

0 

27 

200 

20 

717 

16 

28 

1 

72 

1390 

38 

525 

38 

54 

0 

28 

178 

22 

733 

16 

28 

0 

73 

1427 

37 

485 

40 

54 

0 

29 

156 

22 

749 

16 

28 

0 

74 

1463 

36 

444 

41 

54 

0 

23 

15 

1 

35 

43 

-1 

30 

-133 

4764 

+29 

75 

41498 

4401 

453 

31 

109 

424 

779 

415 

29 

40 

76 

1532 

434 

356 

-45 

53 

-0 

32 

85 

24 

793 

14 

29 

0 

77 

1564 

32 

310 

46 

53 

0 

33 

60 

25 

807 

14 

30 

1 

78 

1595 

31 

262 

48 

52 

1 

34 

34 

26 

821 

14 

30 

0 

79 

1625 

30 

212 

60 

51 

1 

35 

-    8 

26 

834 

13 

31 

1 

80 

1653 

28 

161 

51 

51 

0 

36 

4  20 

28 

847 

13 

31 

0 

81 

1680 

27 

108 

53 

50 

1 

37 

48 

28 

859 

12 

32 

1 

82 

1705 

25 

4  54 

54 

49 

1 

38 

77 

29 

870 

11 

32 

0 

83 

1729 

24 

-    2 

56 

47 

2 

39 

107 

30 

881 

11 

33 

1 

84 

1751 

22 

59 

57 

46 

1 

30 

10 

0 

20 

59 

1 

40 

+137 

4891 

+33 

85 

41771 

-118 

445 

41 

169 

432 

900 

4  9 

34 

41 

86 

1789 

418 

178 

-60 

43 

-2 

42 

201 

32 

908 

8 

35 

1 

87 

1805 

16 

239 

61 

41 

2 

43 

234 

33 

916 

8 

35 

0 

88 

1819 

14 

301 

62 

40 

1 

44 

268 

34 

923 

7 

36 

1 

89 

1831 

12 

365 

64 

38 

2 

45 

4303 

435 

4928 

4  6 

+37 

4l 

90 

410 

-64 

+36 

-2 

TABLE    IV.—  Continued, 

IM.Ull  UP.  \TIo.\S  OF  TIIK  CO-OKDINATKS  IN  UMTS  OF  THE   SIXTH   DECIMAL. 

AROUMKNT  I. 

t 

Dilf. 

1l 

Diir. 

fi 

Diff. 

Atg. 

i. 

Diff. 

ft 

Diff. 

fi 

Diff. 

o 
90 

•1-11 

-  420 

+  36 

0 

135 

-  408 

teat 

-116 

n 

1848 

+  7 

-«• 

34 

-«• 

136 

506 

-98 

2H40 

-    l 

11!) 

-a 

03 

1864 

a 

561 

i 

31 

* 

137 

605 

M 

+   a 

122 

i 

93 

l-',7 

+  i 

M 

• 

89 

1 

138 

704 

W 

2831 

a 

125 

3 

94 

iaa 

0 

6% 

• 

37 

•i 

139 

80S 

|| 

MM 

n 

127 

9 

•'.'. 

-  i 

765 

,  • 

84 

3 

140 

902 

M 

•_'-.  <; 

14 

130 

a 

96 

i--,i 

i 

634 

oe 

21 

3 

141 

101)1 

•„ 

•J7-- 

18 

132 

a 

97 

i-ii 

7 

904 

- 

18 

3 

142 

1100 

'• 

2767 

9) 

134 

a 

96 

i  -  ..-, 

• 

•>::. 

:i 

i:. 

* 

143 

1198 

2741 

. 

136 

I 

99 

1333 

11 

mi 

70 

12 

a 

144 

1295 

»7 

2712 

•it 

138 

* 

IS 

71 

a 

90 

S3 

« 

100 

+1806 

-1116 

+    9 

145 

-1391 

-2679 

-140 

101 

17'l 

-17 

1187 

-71 

6 

-» 

146 

1487 

-•• 

2643 

+  ai 

141 

-i 

m 

1771 

-.11 

• 

+    3 

* 

147 

l.'.-l 

II 

2608 

40 

143 

9 

103 

1748 

• 

i::  1,1 

71 

0 

» 

14- 

1674 

••. 

KM 

44 

144 

1 

104 

17-23 

1401 

71 

-    4 

4 

MB 

1766 

W 

2510 

48 

145 

1 

105 

I6M 

• 

1471 

70 

7 

I 

150 

!-:,(, 

M 

MM 

61 

146 

1 

106 

i.,  ,i 

ai 

1542 

71 

11 

4 

161 

1944 

88 

2405 

M 

147 

1 

107 

16« 

u 

1612 

70 

14 

t 

152 

2030 

• 

2347 

- 

148 

1 

108 

i:.-  i 

17 

n,-l 

,', 

18 

4 

153 

2114 

84 

2286 

61 

148 

0 

109 

i:,i- 

41 

171'' 

23 

4 

154 

2196 

SI 

2221 

M 

149 

-1 

41 

• 

t 

80 

<•-, 

0 

110 

hUM 

-1817 

-  35 

155 

-2276 

-2154 

-149 

111 

n  .- 

-4« 

1-:! 

-«• 

29 

-4 

156 

2tr>4 

-18 

2083 

+  71 

149 

0 

11-.' 

14W 

i  i 

1949 

M 

33 

4 

ir.7 

2429 

-  • 

2009 

74 

149 

0 

Ill 

li-tf 

S3 

2013 

64 

37 

4 

158 

9501 

72 

1!I33 

76 

148 

4i 

IM 

1301 

• 

•J  '7.-. 

• 

41 

4 

159 

2571 

70 

1854 

•9 

148 

0 

iir. 

r.'i:t 

• 

2136 

81 

45 

4 

160 

tea 

M 

1772 

• 

147 

I 

in; 

1  1  -.• 

«1 

•JI'HJ 

00 

48 

t 

161 

2701 

«4 

1688 

84 

146 

1 

117 

m- 

M 

2253 

57 

4 

162 

2762 

• 

1601 

87 

145 

1 

118 

1052 

M 

2309 

M 

56 

4 

163 

2819 

• 

1512 

8» 

144 

1 

11  ' 

M 

at 

Ha 

• 

60 

4 

164 

•-'-71 

&4 

1420 

K 

143 

1 

-.: 

• 

4 

SI 

«a 

9 

130 

•   Oil 

-2414 

-64 

165 

-2925 

-1327 

-141 

l-.'l 

-17 

-74 

M63 

-49 

68 

-4 

166 

2973 

-4« 

1232 

+  M 

140 

+  1 

m 

760 

77 

4« 

72 

4 

167 

3017 

44 

1135 

87 

138 

2 

123 

681 

79 

8553 

44 

75 

1 

168 

MM 

41 

1036 

09 

136 

2 

IM 

600 

81 

MM 

41 

79 

4 

169 

3095 

37 

935 

101 

134 

2 

IX 

516 

81 

HH 

H 

83 

4 

170 

3128 

,; 

833 

10* 

132 

2 

1-36 

431 

81 

nee 

M 

86 

3 

171 

3158 

H 

730 

H3 

12» 

3 

127 

344 

87 

2701 

;i 

90 

4 

172 

3184 

2« 

M 

104 

127 

2 

128 

M 

-  ' 

2730 

• 

94 

4 

173 

3206 

• 

521 

IM 

124 

3 

129 

164 

91 

2756 

24 

97 

3 

174 

3224 

18 

414 

107 

121 

a 

•• 

99 

3 

IS 

107 

a 

130 

+    71 

•4778 

-100 

175 

-3239 

-  307 

-118 

131 

-    22 

-«• 

ma 

-i» 

104 

-4 

176 

3249 

-10 

200 

+  107 

115 

•fa 

132 

117 

M 

2813 

it 

107 

I 

177 

3255 

« 

-    98 

108 

112 

a 

133 

213 

M 

•j-r, 

19 

110 

3 

178 

3258 

-  1 

+     17 

IM 

109 

a 

134 

310 

• 

MM 

1 

113 

3 

179 

3256 

+  a 

125 

108 

105 

4 

135 

-  408 

-t» 

••-:;•  i 

-  t 

-116 

-t 

180 

MN 

+  « 

+  234 

+  109 

-102 

+a 

46 


TABLE    IV.—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  I. 

Arg. 

& 

Diff. 

»h 

Diff. 

tl 

Diff. 

Arg. 

Ji 

Diff. 

ft 

Diff. 

& 

Diff. 

0 

O 

180 

-3251 

+  234 

-102 

225 

+  122 

+2878 

+78 

181 

3241 

+  10 

342 

+108 

98 

+4 

226 

220 

+98 

2857 

-51 

80 

+2 

182 

3228 

13 

450 

108 

94 

4 

227 

316 

96 

2832 

25 

82 

2 

18 

108 

3 

95 

183 

3210 

558 

91 

228 

411 

2804 

2o 

84 

2 

184 

3188 

22 

664 

106 

87 

4 

229 

505 

94 

2773 

31 

86 

I 

185 

3163 

25 

771 

107 

83 

4 

230 

596 

91 

2738 

35 

88 

2 

186 

3133 

30 

876 

105 

79 

4 

231 

686 

90 

2700 

38 

90 

2 

187 

3099 

34 

980 

104 

75 

4 

232 

774 

88 

2659 

41 

92 

2 

188 

3062 

37 

1083 

103 

70 

5 

233 

859 

85 

2615 

44 

93 

1 

189 

3020 

42 

1184 

101 

66 

4 

234 

942 

63 

2568 

47 

94 

1 

45 

100 

4 

61 

50 

1 

190 

-2975 

+1284 

-  62 

235 

+1023 

+2518 

+95 

191 

2926 

4-  49 

1382 

+  98 

57 

+5 

236 

1101 

+78 

2466 

-53 

96 

+  1 

192 

2874 

52 

1478 

96 

53 

4 

237 

1177 

76 

2411 

65 

97 

1 

193 

2817 

57 

1572 

94 

49 

4 

238 

1250 

73 

2354 

57 

98 

1 

194 

2758 

59 

1664 

92 

44 

6 

239 

1320 

70 

2294 

60 

98 

0 

195 

2695 

63 

1754 

90 

40 

4 

240 

1388 

68 

2233 

61 

98 

0 

196 

2628 

67 

1841 

87 

35 

5 

241 

1453 

65 

2169 

64 

98 

0 

197 

2558 

70 

1926 

85 

31 

4 

242 

1514 

61 

2103 

66 

99 

+1 

198 

2485 

73 

2008 

82 

26 

5 

243 

1573 

59 

2036 

67 

98 

-1 

199 

2410 

75 

2087 

79 

22 

4 

244 

1629 

56 

1967 

69 

98 

0 

79 

76 

5 

53 

71 

0 

200 

-2331 

+2163 

-  17 

245 

+1682 

+18P6 

+98 

201 

2249 

+  82 

2236 

+  73 

13 

+4 

246 

1732 

+50 

1824 

-72 

97 

-1 

202 

2165 

84 

2306 

70 

8 

5 

247 

1778 

46 

1751 

73 

97 

0 

203 

2079 

86 

2372 

66 

-    4 

4 

248 

1822 

44 

1676 

75 

96 

1 

204 

1990 

89 

2435 

63 

+    1 

5 

249 

1862 

40 

1601 

75 

95 

1 

205 

1899 

91 

2495 

60 

5 

4 

250 

1899 

37 

1524 

77 

94 

1 

206 

1806 

93 

2551 

56 

10 

5 

251 

1933 

34 

1447 

77 

93 

1 

207 

1711 

95 

2603 

52 

14 

4 

252 

1963 

30 

1369 

78 

92 

1 

208 

1614 

97 

2651 

48 

18 

4 

253 

1990 

27 

1291 

78 

90 

2 

209 

1516 

98 

2696 

45 

23 

5 

254 

2015 

25 

1212 

79 

89 

1 

99 

41 

4 

20 

78 

2 

210 

-1417 

+2737 

+  27 

255 

+2035 

+1134 

+87 

211 

1316 

+101 

2774 

+  37 

31 

+4 

256 

2053 

+18 

1055 

-79 

86 

-1 

212 

1214 

102 

2807 

33 

35 

4 

257 

2067 

14 

976 

79 

84 

2 

213 

1112 

102 

2836 

29 

39 

4 

258 

2079 

12 

897 

79 

82 

2 

214 

1008 

104 

2861 

25 

43 

4 

259 

2087 

8 

818 

79 

80 

2 

•215 

905 

103 

2882 

21 

46 

3 

260 

2093 

6 

740 

78 

78 

2 

216 

801 

104 

2900 

18 

50 

4 

261 

2095 

+  2 

663 

77 

76 

2 

217 

697 

104 

2913 

13 

54 

4 

262 

2094 

-  1 

586 

77 

74 

2 

218 

593 

104 

2922 

9 

57 

3 

263 

2090 

4 

509 

77 

72 

3 

219 

489 

104 

2927 

5 

60 

3 

264 

2083 

7 

434 

75 

70 

2 

104 

+     2 

3 

9 

74 

2 

223 

-  385 

+2929 

+  63 

265 

+2074 

+  360 

+68 

221 

282 

+103 

2926 

-     3 

67 

+4 

266 

2061 

-13 

286 

-74 

66 

-2 

222 

180 

102 

2920 

6 

70 

3 

267 

2046 

15 

214 

72 

63 

3 

223 

-    78 

102 

2910 

10 

72 

2 

268 

2029 

11 

143 

71 

61 

2 

224 

+    22 

100 

2896 

14 

75 

3 

269 

2008 

21 

74 

69 

59 

2 

225 

+  122 

+  100 

+2878 

-  18 

+  78 

+3 

270 

+1985 

-23 

+      6 

-68 

+56 

-3 

47 


V    ^      v  *5lkS77»T*]\ 

TABLE     IV.—  ConHnnnl. 

I'KinVK!'.  VTHiNS  OF  TIIK  COORDINATES   IN   r.MTs  oF  TIIK   SIXTH   DECIMAL. 

ARGUMENT   I. 

Ar_- 

ft 

Dirt; 

t. 

Diff. 

b 

Diff. 

Arg. 

ft 

Diff. 

'.: 

Diff. 

Cl 

Diff. 

o 

o 

-'7  n 

+     6 

+56 

-  90 

-969 

-10 

'.'71 

1981 

-9» 

-    61 

-ft 

54 

"* 

316 

55 

-i* 

+  18 

9 

+1 

m 

27 

126 

89 

n 

1 

317 

89 

M 

M 

19 

9 

0 

I'M:! 

I 

l-.i 

61 

4!) 

* 

318 

129 

n 

.•'• 

8 

l 

274 

1-71 

12 

m 

61 

46 

1 

B9 

154 

884 

21 

8 

0 

l-:t7 

14 

309 

. 

44 

1 

BH 

]-:. 

31 

21 

7 

i 

ua 

19 

367 

98 

42 

1 

321 

•Ji:. 

M 

841 

.. 

6 

i 

m 

I7M 

I 

422 

99 

39 

i 

322 

243 

•- 

-1- 

*» 

6 

0 

278 

17-:. 

'  . 

475 

91 

37 

2 

323 

•.'7  n 

27 

795 

5 

1 

K.-l 

41 

M 

: 

34 

1 

324 

296 

-. 

771 

M 

4 

1 

41 

49 

2 

29 

94 

1 

•J-i 

+1641 

-  576 

+32 

325 

-321 

-747 

-  3 

•J-I 

-44 

623 

-47 

30 

—1 

326 

345 

-24 

722 

+28 

2 

+1 

M 

49 

668 

49 

27 

1 

327 

366 

-  i 

697 

. 

1 

1 

•-'-:: 

47 

710 

49 

25 

2 

BB8 

390 

22 

671 

.. 

-  1 

0 

•j-l 

1  1.-.- 

47 

750 

40 

23 

2 

329 

410 

-• 

645 

•'• 

0 

1 

1409 

49 

7- 

M 

21 

9 

330 

430 

20 

619 

... 

+  1 

1 

1360 

-Jl 

M 

18 

1 

331 

448 

18 

593 

... 

2 

1 

•.'-: 

nut 

I 

857 

n 

16 

9 

332 

465 

n 

566 

27 

3 

1 

•j-- 

1980 

91 

--- 

11 

14 

9 

333 

481 

16 

539 

27 

4 

1 

out 

91 

916 

" 

12 

9 

334 

497 

1 

512 

97 

5 

1 

99 

28 

9 

14 

27 

1 

ZX) 

+  1  1  ."><j 

-  942 

+10 

335 

-511 

-485 

+  6 

•J'l 

I1M 

-99 

B8B 

:i 

8 

-9 

336 

524 

-11 

458 

+97 

7 

+1 

9J 

BOB 

22 

7 

1 

337 

536 

12 

431 

27 

8 

1 

U 

1008 

." 

5 

9 

338 

:.!- 

12 

403 

-'- 

8 

0 

•J  '1 

947 

99 

1025 

17 

3 

9 

339 

558 

10 

376 

27 

9 

1 

-c, 

M 

1040 

19 

+  2 

1 

340 

567 

9 

348 

• 

10 

1 

m 

843 

I 

IM 

11 

0 

2 

341 

576 

9 

321 

27 

11 

1 

•J"7 

791 

11 

1064 

11 

-  1 

1 

342 

583 

7 

293 

28 

12 

1 

998 

740 

91 

1072 

- 

2 

1 

343 

590 

7 

266 

27 

12 

0 

•J" 

t.-i 

91 

1079 

7 

4 

9 

344 

595 

6 

239 

27 

13 

1 

91 

I 

) 

8 

28 

1 

300 

+  638 

lii-l 

-  5 

345 

-600 

-211 

+14 

301 

BBS 

-ao 

1689 

-  1 

6 

-1 

346 

8M 

-  4 

184 

+27 

14 

+0 

302 

am 

49 

1088 

~  ' 

7 

1 

347 

607 

I 

157 

27 

U 

1 

m 

490 

49 

1087 

+  1 

7 

0 

348 

609 

2 

130 

27 

16 

1 

304 

443 

47 

1085 

2 

8 

1 

349 

611 

-  2 

103 

27 

16 

0 

305 

396 

47 

1081 

4 

9 

1 

350 

611 

0 

77 

26 

17 

1 

306 

350 

48 

ion 

8 

9 

0 

351 

611 

0 

50 

27 

17 

0 

307 

304 

48 

1064 

7 

10 

-1 

3T>2 

610 

+  1 

-  24 

28 

18 

1 

308 

•y,  • 

44 

1059 

9 

10 

0 

3T>3 

609 

1 

+    9 

28 

18 

0 

309 

217 

41 

1049 

10 

10 

0 

3T>4 

606 

1 

98 

28 

19 

1 

42 

12 

0 

1 

29 

0 

310 

+   17.', 

-1037 

-10 

355 

-603 

+  53 

+19 

311 

134 

-41 

in-JI 

+11 

10 

0 

356 

599 

+  4 

79 

+26 

19 

+0 

312 

94 

40 

1010 

14 

10 

0 

357 

595 

4 

104 

29 

20 

1 

313 

55 

to 

0M 

19 

10 

0 

358 

590 

* 

129 

99 

90 

0 

314 

+    17 

M 

TOI 

18 

10 

0 

3.11  1 

584 

G 

153 

24 

20 

0 

315 

-    20 

-n 

-  962 

+  17 

-10 

0 

360 

-577 

+  7 

+177 

+44 

••.'l 

+1 

48 


TABLE    IV.  —  Continued. 

PEETURBATIONS  OF  THE  CO-ORDINATES  IN  UJJITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  II. 

Arg. 

Ji 

Diff. 

»h 

Diff. 

fl 

Diff. 

Arg. 

6 

Diff. 

m 

Diff. 

& 

Diff. 

o 

o 

0 

+551 

+  51 

-38 

45 

+  118 

+727 

-23 

1 

550 

-  i 

65 

+  14 

37 

+1 

46 

92 

~16 

739 

+12 

23 

-o 

2 

548 

4 

78 

13 

37 

0 

47 

66 

26 

750 

11 

23 

0 

3 

547 

i 

91 

13 

36 

i 

48 

39 

27 

760 

10 

24 

i 

4 

546 

i 

105 

14 

35 

i 

49 

+    12 

27 

769 

9 

24 

0 

5 

544 

2 

118 

13 

34 

i 

50 

-    17 

29 

777 

8 

24 

0 

6 

542 

3 

134 

14 

34 

0 

51 

46 

29 

785 

8 

24 

0 

7 

540 

2 

146 

14 

33 

1 

52 

76 

30 

791 

6 

25 

1 

• 

14 

t 

On 

8 

538 

160 

32 

53 

106 

oU 

797 

0 

25 

0 

9 

536 

2 

174 

14 

31 

i 

54 

137 

31 

802 

6 

25 

0 

2 

14 

0 

32 

3 

1 

10 

+534 

+188 

-31 

55 

-  169 

+805 

-26 

11 

531 

-  3 

202 

+14 

30 

+1 

56 

201 

-32 

808 

+  3 

26 

-o 

12 

528 

3 

217 

15 

29 

1 

57 

233 

32 

810 

+  2 

26 

0 

13 

525 

3 

231 

14 

28 

1 

58 

266 

33 

810 

0 

27 

1 

14 

521 

4 

246 

15 

28 

0 

59 

299 

33 

809 

-  1 

27 

0 

15 

517 

4 

261 

15 

27 

1 

60 

333 

34 

807 

2 

27 

0 

16 

513 

4 

276 

15 

27 

0 

61 

367 

34 

804 

3 

27 

0 

17 

508 

S 

292 

16 

26 

1 

62 

401 

34 

799 

5 

27 

0 

18 

503 

i 

307 

15 

25 

1 

63 

435 

34 

793 

6 

28 

-1 

19 

498 

6 

323 

16 

25 

0 

64 

470 

35 

786 

7 

28 

0 

0 

16 

1 

34 

8 

0 

20 

+492 

+339 

-24 

65 

-  504 

+778 

-28 

21 

485 

-  7 

355 

+16 

24 

+0 

66 

538 

-34 

768 

-10 

28 

0 

22 

478 

7 

371 

16 

24 

0 

67 

573 

35 

756 

12 

28 

0 

23 

470 

8 

387 

16 

23 

1 

68 

607 

34 

744 

12 

28 

0 

24 

462 

8 

404 

17 

23 

0 

69 

641 

34 

730 

14 

28 

0 

25 

453 

9 

420 

16 

22 

1 

70 

674 

33 

714 

16 

28 

0 

26 

444 

9 

437 

17 

22 

0 

71 

708 

34 

697 

17 

28 

0 

27 

434 

10 

453 

16 

22 

0 

72 

740 

32 

679 

18 

28 

0 

28 

423 

11 

470 

17 

22 

0 

73 

773 

33 

660 

19 

27 

+1 

29 

411 

12 

487 

17 

22 

0 

74 

805 

32 

638 

20 

27 

0 

12 

16 

+1 

31 

22 

0 

30 

+399 

+503 

-21 

75 

-  836 

+616 

-27 

31 

386 

—  13 

520 

+17 

21 

0 

76 

866 

-30 

592 

-24 

26 

+1 

32 

372 

14 

536 

16 

21 

0 

77 

896 

30 

567 

25 

26 

0 

33 

358 

14 

553 

17 

21 

0 

78 

925 

29 

540 

27 

26 

0 

34 

342 

16 

569 

16 

21 

0 

79 

953 

29 

512 

28 

25 

1 

35 

326 

16 

585 

16 

21 

0 

80 

980 

27 

483 

29 

24 

1 

36 

309 

17 

601 

16 

21 

0 

81 

1006 

26 

453 

30 

24 

0 

37 

291 

18 

617 

16 

21 

0 

82 

1031 

25 

421 

32 

23 

1 

38 

273 

18 

632 

15 

21 

0 

83 

1055 

24 

388 

33 

22 

1 

39 

253 

20 

647 

15 

21 

0 

84 

1077 

22 

354 

34 

22 

0 

20 

14 

-1 

21 

35 

1 

40 

+233 

+661 

-22 

85 

-1098 

+319 

-21 

41 

211 

—22 

676 

+15 

22 

0 

86 

1118 

-20 

282 

-37 

20 

+1 

42 

189 

22 

689 

13 

22 

0 

87 

1137 

19 

245 

37 

19 

1 

43 

166 

23 

703 

14 

22 

0 

88 

1154 

17 

206 

39 

18 

1 

44 

142 

24 

715 

12 

22 

0 

89 

1170 

16 

167 

39 

17 

1 

45 

+118 

-24 

+727 

+12 

-23 

1 

90 

-1184 

-14 

+127 

-40 

-15 

+2 

49 


TABLE    IV.—  Continued. 

ri.KTi  mi.vno.Ns  OF  THE  CO-ORDINAI  i>  IN  \  \ns  ur  TIIK  SIXTH  DECIMAL. 

ARGUMENT  II. 

A*. 

fi 

Diff. 

»!l 

Diff. 

& 

ONE 

Arg. 

fc 

Diff. 

It 

Diff. 

tl 

Diff. 

O 

0 

90 

-1184 

+  137 

-15 

UB 

+      5 

MN 

+  76 

91 

I1M 

H 

86 

-41 

14 

+1 

136 

61 

+M 

1424 

•" 

77 

+1 

M 

1207 

11 

44 

49 

13 

i 

137 

117 

56 

1  !.'-. 

~ 

79 

a 

M 

TJII, 

« 

+      1 

43 

11 

i 

138 

174 

67 

1424 

+ 

81 

a 

M 

aau 

7 

i-j 

41 

10 

i 

139 

230 

M 

1421 

83 

a 

m 

1 

85 

41 

9 

i 

140 

266 

M 

1416 

65 

a 

96 

I'.'!-' 

4 

130 

• 

7 

a 

141 

342 

M 

1406 

8 

66 

i 

97 

1£M 

-  1 

174 

44 

5 

a 

142 

398 

M 

1399 

I 

88 

a 

98 

I-.MI 

0 

319 

45 

4 

1 

143 

453 

55 

1387 

la 

89 

i 

99 

+  a 

M 

.•• 

-  3 

a 

144 

509 

56 

1374 

11 

91 

a 

4 

4i 

a 

M 

18 

i 

100 

IM 

-  310 

0 

145 

+  563 

-1358 

+  99 

101 

i  •.-.-,' 

+  6 

356 

-4« 

+  1 

+1 

146 

617 

+44 

1340 

+18 

93 

+1 

IM 

l-'ll 

8 

401 

49 

3 

a 

147 

670 

U 

1320 

•JO 

94 

i 

103 

ISM 

10 

447 

46 

5 

a 

148 

723 

S3 

1298 

aa 

96 

a 

Hi4 

UM 

11 

492 

41 

7 

a 

149 

774 

11 

1274 

a4 

97 

i 

105 

117' 

14 

538 

48 

9 

a 

150 

M 

51 

1248 

36 

96 

1 

106 

1163 

16 

583 

45 

11 

a 

ir.l 

-7:. 

50 

1231 

97 

99 

i 

107 

1146 

n 

627 

44 

13 

a 

152 

923 

48 

1191 

30 

99 

0 

106 

1136 

.'• 

671 

44 

15 

a 

153 

97J 

48 

1159 

I 

100 

i 

109 

1104 

:: 

715 

44 

17 

a 

154 

1017 

4« 

1126 

n 

101 

i 

n 

41 

i 

44 

u 

0 

110 

-1061 

-  758 

+20 

155 

+1061 

-1091 

+101 

111 

1056 

+» 

-0,1 

-42 

33 

+a 

156 

1105 

+44 

1054 

+n 

102 

+1 

11-J 

1038 

• 

843 

43 

84 

a 

157 

1147 

4a 

1016 

18 

102 

0 

113 

• 

40 

26 

a 

158 

1187 

40 

976 

40 

102 

0 

114 

968 

• 

923 

40 

99 

i 

159 

1325 

38 

934 

43 

102 

0 

115 

936 

»a 

961 

39 

31 

a 

160 

1262 

i; 

891 

43 

103 

+1 

116 

'Ml 

H 

999 

18 

33 

a 

161 

1297 

15 

847 

44 

103 

0 

117 

m 

i  , 

1035 

• 

35 

a 

162 

1330 

• 

801 

• 

103 

-1 

118 

~.'7 

:l- 

1070 

Si 

38 

i 

163 

1363 

la 

755 

46 

102 

0 

11:' 

788 

M 

1104 

14 

40 

a 

164 

1391 

a* 

707 

48 

102 

0 

41 

U 

9 

38 

M 

0 

m 

-747 

-1137 

+49 

165 

+1419 

-  657 

+103 

rji 

705 

+49 

1168 

-11 

46 

+1 

166 

1445 

+96 

607 

+tt 

101 

-1 

122 

661 

44 

1197 

a» 

47 

a 

167 

146S 

• 

556 

51 

101 

0 

133 

616 

41 

1325 

.- 

49 

a 

168 

1489 

91 

504 

59 

100 

1 

134 

MR 

47 

1253 

37 

52 

i 

169 

1509 

ao 

Ml 

53 

99 

1 

135 

• 

47 

1277 

54 

a 

170 

1526 

n 

M 

54 

99 

0 

136 

473 

• 

1300 

:i 

56 

a 

171 

1541 

15 

344 

54 

98 

1 

137 

1-.". 

M 

1331 

31 

59 

i 

172 

1554 

n 

390 

54 

97 

1 

138 

372 

81 

1340 

19 

61 

i 

173 

1564 

10 

235 

U 

96 

1 

139 

.'.-.'  i 

M 

1357 

17 

63 

a 

174 

1573 

» 

179 

58 

96 

1 

51 

18 

a 

6 

55 

a 

130 

-  267 

-1373 

465 

175 

+1579 

-  134 

+  93 

131 

314 

+« 

IM 

-11 

67 

+9 

176 

1563 

+  i 

68 

+M 

93 

-i 

133 

160 

M 

1398 

11 

69 

a 

177 

1584 

+  a 

13 

58 

91 

i 

133 

106 

1408 

10 

73 

i 

178 

1583 

~  ' 

+    44 

56 

90 

i 

134 

-    50 

M 

1415 

7 

74 

a 

179 

l.-.-u 

i 

100 

50 

86 

a 

m 

•       -'. 

+M 

1490 

+  5 

+76 

+a 

180 

U575 

+  156 

+5« 

+  87 

-i 

50 


TABLE    IV  .—Continued. 

PERTURBATIONS  OP  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  II. 

Arg. 

ft 

Diff. 

* 

Diff. 

fl 

Diff. 

Arg. 

li 

Diff. 

% 

Diff. 

?! 

Diff. 

o 

o 

180 

+1575 

+  156 

+87 

225 

-  291 

+1353 

-  6 

181 

1567 

-  8 

211 

+55 

85 

-2 

226 

342 

-51 

1337 

-16 

8 

-2 

182 

1557 

10 

266 

55 

83 

2 

227 

393 

61 

1318 

19 

10 

2 

183 

1545 

12 

321 

55 

82 

1 

228 

443 

50 

1298 

20 

11 

1 

184 

1531 

14 

375 

54 

80 

2 

229 

492 

49 

1276 

22 

12 

1 

185 

1514 

17 

428 

63 

78 

2 

230 

539 

47 

1252 

24 

14 

2 

186 

1496 

18 

481 

53 

76 

2 

231 

586 

47 

1226 

26 

15 

1 

187 

1475 

21 

533 

52 

74 

2 

232 

631 

45 

1199 

27  . 

17 

2 

188 

1452 

23 

584 

51 

72 

3 

233 

675 

44 

1170 

29 

18 

1 

189 

1427 

25 

635 

51 

70 

2 

234 

717 

42 

1140 

30 

19 

1 

27 

49 

2 

41 

32 

1 

190 

+1400 

+  684 

+68 

235 

-  758 

+1108 

-20 

191 

1372 

-28 

732 

+48 

66 

-2 

236 

798 

-40 

1075 

-33 

21 

-1 

192 

1341 

31 

779 

47 

64 

3 

237 

836 

38 

1040 

35 

22 

1 

193 

1308 

33 

825 

46 

62 

2  • 

238 

872 

36 

1004 

36 

23 

1 

194 

1274 

34 

870 

45 

60 

3 

239 

907 

35 

967 

37 

24 

1 

195 

1238 

36 

913 

43 

57 

3 

240 

940 

33 

929 

38 

25 

1 

196 

1200 

33 

955 

42 

55 

2 

241 

971 

31 

890 

39 

26 

1 

197 

1160 

40 

995 

40 

53 

2 

242 

1001 

30 

850 

40 

27 

1 

198 

1119 

41 

1033 

38 

51 

2 

243 

1028 

27 

809 

41 

27 

0 

199 

1076 

43 

1071 

38 

48 

3 

244 

1054 

26 

767 

42 

28 

1 

44 

35 

2 

24 

43 

1 

200 

+1032 

^ 

+1106 

+46 

245 

-1078 

+  724 

-29 

201 

987 

-45 

1140 

+34 

44 

-3 

246 

1100 

-22 

681 

-43 

29 

-o 

202 

941 

46 

1172 

32 

41 

3 

247 

1120 

20 

637 

44 

30 

1 

203 

893 

48 

1202 

30 

39 

2 

248 

1138 

18 

593 

44 

30 

0 

204 

844 

49 

1230 

28 

37 

3 

249 

1154 

16 

548 

45 

31 

1 

205 

794 

50 

1256 

26 

34 

3 

250 

1168 

14 

503 

45 

31 

0 

206 

743 

51 

1281 

25 

32 

3 

251 

1181 

13 

458 

45 

32 

1 

207 

691 

62 

1303 

22 

30 

3 

252 

1191 

10 

412 

46 

32 

0 

208 

639 

52 

1324 

21 

28 

2 

253 

1199 

8 

367 

45 

32 

0 

209 

585 

64 

1342 

18 

25 

3 

254 

1205 

6 

321 

46 

33 

1 

64 

16 

2 

6 

45 

0 

210 

+  531 

+1358 

+23 

255 

-1210 

+  276 

-33 

211 

477 

-54 

1373 

+15 

21 

-2 

256 

1212 

—  2 

230 

-46 

33 

-o 

212 

422 

55 

1385 

12 

19 

2 

257 

1213 

-  1 

185 

45 

33 

0 

213 

367 

55 

1395 

10 

17 

2 

258 

1211 

+  3 

141 

44 

33 

0 

214 

311 

56 

1403 

8 

15 

3 

259 

1208 

3 

96 

45 

34 

1 

215 

256 

55 

1409 

6 

12 

3 

260 

1203 

5 

52 

44 

34 

0 

216 

200 

56 

1413 

4 

10 

3 

261 

1196 

7 

+      9 

43 

34 

0 

217 

144 

56 

1414 

+  1 

8 

3 

262 

1187 

9 

-    34 

43 

34 

0 

218 

89 

55 

1414 

0 

6 

2 

263 

1177 

10 

76 

42 

34 

0 

219 

+    33 

66 

1412 

-  2 

4 

2 

264 

1165 

13 

118 

42 

34 

0 

65 

5 

1 

14 

40 

0 

220 

-    22 

+1407 

+  3 

265 

-1151 

-  158 

-34 

221 

77 

-56 

1400 

-  7 

+  1 

-2 

266 

1136 

+  15 

198. 

-40 

34 

-o 

222 

131 

64 

1391 

9 

-  1 

2 

267 

1119 

17 

237 

39 

34 

0 

223 

185 

54 

1381 

10 

3 

2 

268 

1101 

18 

274 

37 

34 

0 

224 

238 

53 

1368 

13 

5 

2 

269 

1081 

20 

311 

37 

34 

0 

225 

-  231 

—53 

+1353 

-15 

-6 

-1 

270 

-1060 

+21 

-  347 

-36 

-34 

-o 

51 


TABLE    IV.—  Continued. 

IT.UTt  Kr.ATloNS  OF  T1IK  CO-ORDIN  A  TI.S  IN   1MTS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT   11. 

Arg. 

fi 

Ditr. 

* 

KilV 

& 

Diff. 

Aig. 

t 

Diff. 

* 

Diff. 

b 

Diff. 

o 

o 

270 

-1060 

-347 

-34 

315 

.  986 

-647 

-46 

271 

1037 

4» 

:•.-•.' 

-u 

34 

~* 

316 

305 

4so 

631 

4l« 

46 

-o 

272 

1U13 

34 

415 

S3 

34 

0 

317 

324 

19 

615 

16 

46 

0 

aee 

3A 

447 

13 

34 

0 

318 

M 

18 

599 

16 

47 

i 

•r,\ 

962 

M 

478 

11 

34 

0 

319 

359 

17 

683 

16 

47 

0 

vrr:, 

!>:t5 

.: 

MM 

10 

34 

0 

320 

375 

18 

566 

17 

48 

1 

276 

007 

.- 

536 

:- 

34 

0 

321 

301 

16 

549 

17 

48 

0 

277 

-T- 

-  ' 

564 

II 

34 

0 

322 

405 

14 

532 

17 

48 

0 

273 

-1- 

to 

|  H  I 

an 

34 

0 

323 

419 

U 

.-,7:, 

17 

49 

1 

01 

818 

10 

614 

34 

34 

0 

324 

432 

11 

Me 

17 

49 

0 

3-J 

31 

0 

13 

17 

0 

MO 

7-.; 

-637 

-34 

325 

4444 

-481 

-49 

2S1 

4M 

668 

-ai 

34 

-o 

326 

455 

411 

463 

418 

49 

-o 

M 

722 

n 

.,7-* 

30 

84 

0 

827 

466 

11 

446 

17 

60 

-1 

981 

aee 

S3 

607 

19 

34 

0 

328 

476 

10 

429 

17 

60 

0 

•j-i 

IK 

14 

714 

17 

34 

0 

329 

485 

9 

412 

17 

50 

0 

•>:.          i.-Ji 

14 

730 

18 

36 

1 

330 

493 

8 

394 

18 

60 

0 

'J—  1  1              .">—  7 

34 

744 

14 

35 

0 

331 

601 

8 

377 

17 

50 

0 

•-'-7 

652 

U 

787 

It 

35 

0 

332 

508 

7 

360 

17 

50 

0 

517 

15 

769 

13 

35 

0 

333 

514 

« 

343 

17 

60 

0 

HO 

483 

14 

779 

10 

36 

0 

334 

620 

« 

327 

16 

60 

0 

U 

9 

1 

A 

17 

0 

293 

-  448 

-788 

-36 

335 

4525 

-310 

—50 

291 

413 

4iA 

790 

-  7 

36 

-0 

336 

530 

4  » 

294 

418 

50 

0 

292 

::?- 

34 

801 

6 

36 

0 

337 

534 

4 

277 

17 

50 

0 

203 

:;il 

31 

806 

A 

36 

0 

338 

538 

4 

261 

16 

60 

0 

•."I 

MM 

15 

810 

4 

37 

1 

339 

541 

1 

245 

16 

60 

0 

275 

34 

812 

a 

37 

0 

340 

544 

a 

230 

1A 

49 

4i 

.»•  , 

241 

M 

813 

-  i 

37 

0 

341 

547 

i 

214 

16 

49 

0 

297 

208 

t3 

813 

0 

38 

1 

342 

549 

a 

199 

15 

49 

0 

m 

175 

33 

811 

4  a 

38 

0 

343 

551 

a 

184 

15 

49 

0 

299 

143 

I 

809 

3 

38 

0 

344 

652 

i 

169 

15 

48 

1 

81 

4 

1 

i 

15 

0 

300 
301    ' 

-  Ill 
79 

414 

-805 
800 

4  A 

-39 
39 

-o 

345 
346 

4553 
554 

4  1 

-154 
140 

414 

-48 
47 

41 

308 

48 

11 

795 

5 

40 

1 

347 

555 

1 

125 

15 

47 

0 

303 

-    18 

30 

7- 

7 

40 

0 

348 

556 

4  I 

111 

14 

46 

1 

304 

4    12 

to 

780 

8 

40 

0 

349 

556 

0 

97 

14 

46 

0 

305 

41 

39 

772 

8 

41 

1 

350 

556 

0 

83 

14 

45 

1 

306 

69 

38 

762 

10 

41 

0 

351 

556 

0 

69 

14 

45 

0 

307 

96 

37 

752 

10 

42 

1 

352 

556 

0 

66 

13 

44 

1 

308 

123 

37 

741 

11 

42 

0 

353 

556 

0 

42 

14 

43 

1 

309 

148 

3t 

729 

13 

43 

1 

354 

555 

-  1 

29 

It 

43 

0 

35 

13 

0 

o 

14 

1 

310 

4  173 

-717 

-43 

355 

..-..v, 

-  15 

-42 

311 

197 

434 

•  704 

411 

44 

-1 

356 

664 

-  ' 

-    2 

411 

41 

41 

312 

221 

34 

690 

14 

44 

0 

357 

553 

1 

4  11 

11 

40 

1 

313 

243 

33 

676 

14 

45 

1 

:•.:,- 

553 

0 

35 

14 

40 

0 

314 

265 

St 

662 

14 

45 

0 

552 

1 

38 

11 

39 

1 

315 

4  285 

430 

-647 

413 

-46 

-1 

360 

-  1 

4  51 

411 

-38 

4i 

52 


TABLE    IV.  —  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  III. 

Arg- 

Ji 

Diff. 

fll 

Diff. 

Cl 

Diff. 

Arg. 

ft 

Diff. 

1l 

Diff. 

& 

Diff. 

O 

o 

0 

+977 

-196 

+15 

45 

+537 

-829 

-  7 

1 

973 

-  4 

213 

—17 

46 

522 

-15 

838 

-9 

2 

969 

4 

230 

17 

-2 

47 

506 

16 

847 

9 

-2 

3 

965 

4 

247 

11 

13 

48 

491 

15 

856 

9 

9 

4 

960 

5 

264 

17 

49 

475 

16 

865 

9 

5 

955 

5 

281 

17 

1 

50 

460 

15 

873 

8 

1 

6 

950 

5 

298 

17 

12 

51 

444 

16 

881 

8 

10 

• 

16 

16 

g 

7 

945 

314 

52 

428 

889 

8 

939 

6 

331 

17 

1 

53 

412 

16 

896 

7 

2 

9 

933 

6 

347 

16 

11 

54 

395 

17 

903 

7 

12 

6 

17 

16 

7 

10 

+927 

-364 

55 

+379 

-910 

11 

920 

-  7 

380 

-16 

2 

56 

363 

-16 

917 

-7 

1 

12 

913 

7 

396 

16 

9 

57 

346 

17 

923 

6 

13 

13 

906 

7 

412 

16 

58 

329 

17 

929 

6 

g 

16 

1 

17 

g 

14 

898 

428 

59 

312 

935 

. 

15 

890 

8 

444 

16 

8 

60 

296 

16 

941 

6 

14 

16 

882 

8 

459 

15 

61 

279 

17 

946 

5 

17 

874 

8 

475 

16 

2 

62 

261 

19 

951 

5 

2 

18 

865 

9 

490 

15 

6 

63 

244 

17 

955 

4 

16 

19 

856 

9 

505 

15 

64 

227 

17 

960 

5 

9 

15 

1 

17 

4 

1 

20 

+847 

-520 

65 

+210 

-964 

21 

838 

-  9 

535 

-15 

5 

66 

192 

-18 

967 

-3 

17 

22 

828 

10 

550 

15 

67 

175 

17 

971 

4 

23 

818 

10 

564 

14 

2 

68 

'  158 

17 

974 

3 

1 

24 

808 

10 

578 

14 

3 

69 

140 

18 

977 

3 

18 

25 

797 

11 

592 

14 

70 

123 

17 

979 

2 

26 

786 

11 

606 

14 

1 

71 

105 

18 

981 

2 

1 

27 

775 

11 

620 

14 

+  2 

72 

87 

18 

983 

2 

19 

28 

764 

11 

633 

13 

73 

70 

17 

985 

2 

29 

752 

19 

647 

14 

2 

74 

52 

18 

986 

1 

1 

12 

13 

17 

1 

30 

+740 

-660 

0 

75 

+  35 

-987 

20 

31 

723 

-12 

673 

-13 

76 

+  17 

-18 

988 

-1 

32 

716 

12 

685 

12 

1 

77 

-    1 

18 

989 

-1 

1 

33 

703 

13 

698 

13 

-  1 

78 

18 

17 

989 

0 

21 

34 

691 

12 

710 

12 

79 

36 

13 

989 

0 

35 

678 

13 

722 

12 

2 

80 

53 

17 

988 

+1 

1 

36 

665 

13 

734 

12 

3 

81 

71 

18 

987 

1 

22 

37 

651 

14 

745 

11 

82 

88 

17 

986 

1 

38 

638 

13 

756 

11 

1 

83 

106 

IS 

985 

1 

1 

39 

624 

11 

768 

19 

4 

84 

123 

17 

983 

2 

23 

14 

11 

18 

2 

40 

+610 

-779 

85 

-141 

-981 

41 

595 

-16 

789 

-10 

2 

86 

158 

-17 

979 

+2 

1 

42 

581 

14 

800 

11 

6 

87 

175 

17 

977 

2 

24 

43 

567 

14 

810 

10 

88 

192 

17 

974 

3 

44 

552 

15 

820 

10 

-1 

89 

209 

17 

971 

3 

-1 

45 

+537 

-15 

-829 

-  9 

-  7 

90 

-226 

-17 

-967 

+4 

-25 

63 


TABLE    I  V.—  Continued. 

PERTURBATIONS  OF  THE  CO-OKDINATKS  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  m. 

A*. 

t 

Diff. 

« 

Diff. 

f. 

Diff. 

At*. 

t 

Diff. 

•Jl 

Diff 

tl 

Diff. 

0 

0 

M 

-226 

-967 

-to 

OB 

-834 

-648 

-27 

91 

343 

-17 

••..I 

+ 

136 

-1-J 

-8 

534 

+14 

M 

ni 

17 

960 

-1 

137 

850 

8 

519 

19 

+« 

277 

17 

m 

96 

138 

see 

8 

;,,,-, 

14 

37 

94 

-."I 

17 

951 

139 

866 

8 

490 

16 

95 

310 

18 

946 

0 

140 

874 

8 

475 

16 

l 

96 

327 

17 

'.Ml 

36 

141 

881 

T 

460 

19 

26 

97 

343 

18 

936 

143 

--- 

7 

445 

16 

96 

M 

18 

Hi 

l 

143 

-.14 

' 

nq 

19 

0 

99 

375 

18 

•'.-I 

37 

144 

901 

7 

415 

19 

36 

18 

8 

| 

18 

100 

-391 

M 

145 

-907 

-399 

101 

407 

-18 

911 

+  7 

0 

146 

913 

~t 

384 

+16 

i 

M 

at 

18 

905 

8 

27 

147 

918 

9 

368 

18 

35 

103 

438 

li 

-•,- 

7 

148 

8M 

8 

353 

18 

104 

454 

18 

890 

8 

-I 

149 

939 

9 

336 

18 

0 

105 

469 

19 

--:: 

7 

38 

150 

933 

4 

320 

10 

35 

106 

l-l 

19 

875 

8 

151 

938 

9 

304 

18 

107 

499 

19 

767 

6 

0 

153 

M 

4 

M; 

16 

I 

106 

513 

14 

an 

8 

38 

153 

946 

4 

273 

18 

34 

109 

528 

19 

850 

1 

154 

950 

4 

355 

17 

14 

» 

0 

1 

16 

1 

110 

-549 

-  11 

155 

-953 

-239 

+  9 

_• 

4-IT 

111 

BBf 

at 

98 

156 

956 

^9 

323 

'  17 

23 

112 

571 

14 

m 

9 

157 

959 

1 

206 

H 

113 

584 

13 

813 

10 

0 

158 

961 

3 

189 

17 

1 

114 

.vi- 

14 

803 

10 

38 

159 

963 

' 

173 

17 

32 

11.-. 

611 

13 

793 

10 

160 

965 

3 

155 

17 

116 

mt 

14 

783 

10 

0 

161 

967 

3 

139 

16 

1 

117 

638 

13 

::.- 

11 

38 

163 

968 

1 

133 

17 

21 

118 

651 

13 

763 

10 

163 

969 

1 

105 

17 

119 

663 

11 

751 

11 

0 

164 

970 

-1 

88 

17 

1 

13 

11 

0 

17 

130 

-676 

-740 

98 

165 

-970 

-  71 

20 

131 

M 

-1» 

na 

+1? 

166 

970 

0 

54 

+17 

123 

700 

11 

717 

11 

0 

167 

970 

0 

37 

17 

1 

133 

711 

11 

705 

H 

98 

168 

970 

0 

30 

17 

19 

134 

m 

13 

693 

13 

169 

969 

+' 

-    3 

17 

135 

734 

11 

i,-l 

13 

t 

170 

968 

1 

+  14 

17 

1 

136 

745 

11 

668 

13 

38 

171 

967 

1 

31 

17 

18 

127 

756 

U 

M 

13 

173 

965 

5 

48 

17 

128 

767 

U 

643 

13 

« 

173 

964 

1 

65 

17 

1 

139 

777 

18 

630 

IS 

98 

174 

963 

3 

83 

17 

17 

11 

14 

3 

17 

130 

-787 

-616 

175 

-959 

+  99 

131 

797 

-11 

603 

+  13 

0 

176 

at 

+1 

116 

+  17 

t 

133 

806 

* 

r,!»o 

13 

98 

177 

.,-,! 

3 

133 

17 

15 

133 

816 

11 

576 

14 

178 

950 

4 

150 

17 

134 

825 

* 

m 

14 

+1 

IT'.I 

947 

3 

166 

16 

+1 

i.r, 

-834 

-  * 

+  14 

-27 

l-'i 

!M3 

+4 

fl«3 

+17 

II 

54 


TABLE    IV  .—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE   SIXTH  DECIMAL. 

ARGUMENT  III. 

Arg. 

b 

Diff. 

111 

Diff. 

tl 

Diff. 

Arg. 

fi 

Diff. 

% 

Diff. 

tl 

Diff. 

o 

o 

180 

-943 

+183 

-14 

225 

-524 

+816 

+  7 

181 

939 

+  4 

200 

+17 

226 

510 

+  14 

826 

+10 

182 

935 

4 

217 

17 

+1 

227 

496 

14 

835 

9 

+1 

183 

930 

5 

233 

16 

13 

228 

482 

14 

844 

9 

8 

184 

925 

5 

250 

17 

229 

467 

15 

853 

9 

185 

920 

5 

266 

16 

l 

230 

453 

14 

862 

9 

2 

186 

915 

5 

283 

17 

12 

231 

438 

15 

871 

9 

10 

187 

909 

6 

299 

16 

232 

423 

15 

879 

8 

188 

903 

6 

315 

16 

2 

233 

409 

14 

.887 

'B 

1 

189 

897 

6 

331 

16 

10 

234 

394 

15 

895 

8 

11 

6 

16 

16 

7 

190 

-891 

+347 

235 

-378 

+902 

191 

884 

+  7 

363 

+16 

1 

236 

363 

+15 

909 

+  7 

1 

192 

877 

7 

379 

16 

9 

237 

348 

15 

916 

7 

12 

193 

870 

7 

395 

16 

238 

332 

16 

923 

7 

194 

663 

7 

411 

16 

1 

239 

317 

15 

929 

6 

2 

195 

855 

8 

426 

15 

8 

240 

301 

16 

935 

6 

14 

196 

847 

8 

442 

16 

241 

285 

16 

941 

6 

197 

839 

8 

457 

15 

2 

242 

269 

16 

947 

6 

1 

198 

831 

8 

472 

15 

6 

243 

253 

16 

952 

6 

15 

199 

822 

9 

487 

15 

244 

237 

16 

957 

6 

9 

15 

1 

16 

4 

1 

200 

-813 

+502 

245 

-221 

+961 

201 

804 

+  9 

517 

+15 

5 

246 

205 

+16 

966 

+  5 

16 

202 

795 

9 

531 

14 

247 

189 

16 

970 

4 

203 

785 

10 

546 

15 

2 

248 

173 

16 

974 

4 

1 

204 

776 

9 

560 

14 

3 

249 

156 

n 

977 

3 

17 

205 

766 

10 

574 

14 

250 

140 

16 

980 

3 

206 

755 

11 

588 

14 

1 

251 

123 

n 

983 

3 

2 

207 

745 

10 

602 

14 

-  2 

252 

107 

.    16 

986 

3 

19 

.  208 

734 

11 

615 

13 

253 

90 

n 

988 

2 

209 

724 

10 

629. 

14 

2 

254 

74 

16 

990 

2 

1 

11 

13 

17 

2 

210 
211 

-713 
701 

+12 

+642 
655 

+13 

0 

255 
256 

-  57 
40 

+n 

+992 
993 

+  1 

20 

212 

690 

11 

668 

13 

1 

257 

24 

16 

994 

1 

1 

213 

678 

12 

681 

13 

+  1 

258 

-     7 

n 

995 

1 

21 

214 

666 

12 

693 

12 

259 

+  10 

17 

995 

0 

215 

654 

12 

705 

12 

2 

260 

26 

16 

995 

0 

1 

216 

642 

12 

717 

12 

3 

261 

43 

17 

995 

0 

22 

217 

630 

12 

729 

12 

262 

60 

17 

995 

0 

218 

617 

13 

741 

12 

1 

263 

77 

n 

994 

-  1 

1 

219 

604 

13 

752 

11 

4 

264 

93 

16 

993 

1 

23 

13 

11 

n 

2 

220 

-591 

+763 

265 

+110 

+991 

221 

578 

+  13 

774 

+11 

1 

266 

127 

+17 

990 

-  1 

1 

222 

565 

13 

785 

11 

5 

267 

143 

16 

•      988 

2 

24 

223 

551 

14 

796 

11 

268 

160 

17 

985 

3 

224 

538 

13 

806 

10 

+2 

269 

177 

n 

983 

2 

+0 

225 

-524 

+  14 

+816 

+10 

+  7 

27(1 

+193 

+16 

+980 

-  3 

+24 

55 


TABLE    IV.—  Gmtum-,1. 

I'l.UIl  KliATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  HI. 

Arg. 

6 

Diir. 

T,\ 

Diff. 

f, 

Diff. 

lot 

ft 

Diff. 

fll 

Diff. 

tl 

Diff. 

o 

o 

270 

+1W 

.•.-,i 

+24 

315 

+821 

+561 

+28 

01 

210 

+  17 

•.'77 

-  » 

316 

MO 

+  8 

547 

-14 

272 

236 

M 

973 

4 

+l 

317 

840 

10 

533 

14 

-o 

273 

242 

M 

Ml 

4 

25 

318 

849 

9 

518 

It 

28 

274 

KB 

17 

HE 

4 

319 

-:,- 

• 

Ml 

18 

m 

871 

14 

m 

4 

i 

m 

867 

9 

486 

18 

i 

m 

•j>i 

M 

M 

1 

26 

321 

-::. 

8 

471 

19 

27 

277 

m 

M 

951 

I 

• 

883 

t 

455 

18 

•J> 

m 

17 

MI 

a 

0 

323 

891 

8 

439 

16 

0 

279 

340 

16 

940 

6 

26 

324 

899 

8 

423 

16 

27 

It 

6 

7 

16 

•j-,i 

+355 

+934 

325 

+906 

+407 

•>l 

371 

+  16 

M 

-  • 

i 

326 

913 

+  7 

391 

-16 

' 

M 

in 

18 

921 

7 

27 

327 

MO 

7 

375 

16 

26 

M 

403 

M 

915 

8 

MB 

927 

T 

359 

16 

•j-i 

418 

19 

908 

7 

0 

329 

933 

8 

342 

17 

i 

433 

13 

900 

e 

27 

330 

939 

8 

325 

17 

25 

M 

449 

16 

m 

7 

331 

945 

6 

309 

16 

in 

464 

16 

885 

8 

1 

332 

950 

f 

292 

17 

i 

•-•-- 

479 

M 

876 

I 

28 

333 

955 

• 

275 

17 

24 

M 

494 

19 

868 

8 

334 

960 

t 

258 

17 

15 

1 

0 

4 

17 

0 

290 

+509 

+859 

335 

+964 

+241 

291 

523 

+14 

850 

-  9 

28 

336 

969 

+  6 

224 

-17 

24 

2!t2 

533 

I 

841 

9 

337 

973 

4 

206 

18 

210 

552 

M 

831 

10 

0 

Mi 

976 

1 

169 

17 

1 

294 

566 

14 

822 

9 

28 

339 

m 

1 

172 

17 

23 

M 

:,-n 

14 

812 

10 

340 

Mi 

1 

154 

18 

296 

594 

14 

801 

11 

+1 

341 

985 

1 

137 

17 

1 

297 

608 

14 

791 

10 

29 

342 

987 

3 

120 

17 

22 

MO 

621 

II 

780 

11 

343 

989 

1 

102 

18 

299 

635 

14 

769 

11 

0 

344 

991 

1 

84 

18 

1 

11 

11 

1 

17 

300 

+648 

+757 

29 

345 

+993 

+  67 

21 

301 

661 

+1» 

746 

-M 

346 

994 

+  1 

49 

-18 

m 

673 

19 

734 

11 

0 

347 

995 

+  1 

32 

17 

1 

303 

686 

11 

7M 

11 

29 

348 

995 

0 

+  14 

18 

20 

304 

698 

11 

710 

11 

349 

995 

0 

-    4 

18 

305 

711 

1* 

697 

11 

0 

350 

995 

0 

21 

17 

1 

306 

723 

11 

685 

11 

29 

351 

M6 

0 

39 

18 

19 

307 

734 

11 

672 

11 

352 

994 

-  1 

56 

17 

308 

746 

11 

659 

11 

-1 

353 

993 

1 

74 

18 

1 

309 

757 

11 

645 

14 

98 

354 

992 

1 

91 

17 

17 

11 

11 

* 

18 

310 

+768 

+632 

355 

T.filU 

-109 

311 

779 

+  11 

618 

-14 

0 

356 

988 

— 

126 

-17 

1 

312 

790 

11 

604 

14 

28 

3T.7 

985 

144 

18 

16 

313 

801 

11 

590 

14 

358 

963 

161 

17 

314 

811 

10 

576 

14 

0 

359 

980 

178 

17 

-1 

315 

+  -JI 

+10 

+561 

-It 

+28 

360 

+077 

-1% 

-18 

+15 

IT  ABLE    IV.—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  IV. 

Arg. 

6 

Diff. 

1l 

Diff 

& 

Diff. 

Arg. 

£1 

Diff 

1l 

Diff 

t, 

Diff. 

0° 

-775 

+  75 

+38 

o 
45 

-502 

+691 

+  6 

I 

773 

+  2 

90 

+15 

46 

492 

+  10 

702 

+11 

2 

772 

1 

106 

16 

-2 

47 

482 

10 

713 

11 

-4 

3 

770 

2 

121 

15 

36 

48 

471 

11 

723 

10 

+  2 

4 

768 

2 

137 

16 

49 

460 

11 

734 

11 

5 

765 

3 

152 

15 

1 

50 

450 

10 

744 

10 

4 

6 

763 

2 

167 

15 

35 

51 

439 

11 

754 

10 

-  2 

7 

760 

3 

182 

15 

52 

427 

12 

763 

9 

8 

757 

3 

197 

ia 

1 

53 

416 

11 

773 

10 

4 

9 

754 

3 

213 

16 

34 

54 

405 

11 

782 

9 

V       6 

4 

15 

12 

9 

10 

-750 

+228 

55 

-393 

+791 

11 

747 

+  3 

243 

+15 

2 

56 

382 

+11 

800 

+  9 

4 

12 

743 

4 

257 

14 

32 

57 

370 

12 

309 

9 

10 

13 

739 

4 

272 

15 

58 

358 

12 

817 

8 

14 

735 

4 

287 

13 

2 

59 

346 

12 

825 

8 

5 

15 

730 

5 

302 

15 

30 

60 

334 

12 

833 

8 

15 

16 

725 

5 

316 

14 

61 

322 

13 

841 

S 

17 

720 

5 

331 

15 

1 

62 

310 

12 

848 

7 

5 

18 

715 

5 

345 

14 

29 

63 

298 

12 

856 

8 

20 

19 

710 

5 

359 

14 

64 

285 

13 

863 

7 

6 

15 

5 

12 

6 

5 

20 

-704 

+374 

65 

-273 

+869 

21 

699 

+  5 

388 

+14 

27 

66 

260 

+13 

876 

+  7 

25 

22 

693 

6 

402 

14 

67 

248 

13 

882 

6 

23 

687 

6 

416 

14 

3 

68 

235 

13 

888 

6 

5 

24 

680 

7 

430 

14 

25 

69 

222 

13 

894 

6 

30 

25 

674 

6 

443 

13 

70 

209 

13 

899 

5 

26 

667 

7 

457 

14 

2 

71 

196 

13 

904 

5 

5 

27 

660 

7 

470 

13 

23 

72 

183 

13 

909 

5 

35 

28 

653 

7 

484 

14 

73 

170 

13 

914 

5 

29 

645 

8 

497 

13 

3 

74 

157 

13 

918 

4 

6 

7 

13 

13 

4 

30 

-638 

+510 

21 

75 

-144 

+922 

41 

31 

630 

+  8 

523 

+13 

76 

130 

+  14 

926 

+  4 

32 

622 

8 

536 

13 

3 

77 

117 

13 

929 

3 

5 

•33 

614 

8 

549 

13 

18 

78 

103 

14 

932 

3 

46 

34 

605 

9 

562 

13 

79 

90 

13 

935 

3 

35 

597 

8 

574 

13 

3 

80 

76 

14 

937 

2 

6 

36 

588 

9 

587 

13 

15 

81 

63 

13 

940 

3 

52 

37 

579 

9 

599 

12 

82 

49 

14 

942 

2 

38 

570 

9 

611 

13 

3 

83 

35 

14 

943 

1 

5 

39 

561 

9 

623 

12 

12 

84 

21 

14 

944 

1 

57 

9 

12 

13 

1 

40 

-552 

+635 

85 

-    8 

+945 

41 

542 

+  10 

646 

+11 

3 

86 

+    6 

+  14 

946 

+  1 

6 

42 

532 

10 

658 

12 

9 

87 

20 

14 

946 

0 

63 

43 

523 

9 

669 

11 

88 

34 

14 

946 

0 

44 

513 

10 

680 

11 

-3 

89 

48 

14 

946 

0 

-5 

45 

-502 

+11 

+691 

+  11 

+  6 

90 

+  (i',> 

+  14 

+945 

-  1 

-68 

57 


TABLE    IV.—  Continued. 

PKlMTUr.ATIOXS  OF  THE  CO-ORDINA  IKS  IN    I  MT>  til-'  TIIK   SIXTH    DECIMAL. 
ARGUMENT  IV. 

Ai* 

t 

Diff. 

1l 

Diff. 

& 

Diff. 

Aig. 

«i 

Diff. 

1l 

Diff. 

tl 

Diff. 

o 

O 

90 

+  62 

-68 

135 

+678 

+605 

-114 

91 

77 

+u 

944 

-  i 

136 

BM 

+  11 

-14 

02 

•M 

14 

943 

i 

-» 

137 

701 

11 

578 

11 

0 

93 

105 

U 

•'II 

a 

73 

138 

712 

u 

564 

u 

114 

94 

119 

11 

a 

139 

723 

u 

550 

14 

95 

133 

14 

M 

a 

• 

I 

140 

734 

11 

536 

14 

+1 

96 

147 

U 

m 

i 

78 

141 

745 

u 

522 

14 

113 

97 

162 

13 

932 

* 

142 

755 

10 

507 

II 

98 

176 

14 

M 

* 

» 

143 

MB 

10 

493 

14 

1 

99 

.    190 

It 

M 

4 

83 

144 

775 

10 

478 

1ft 

112 

14 

4 

9 

16 

100 

••:••! 

+921 

145 

•7-1 

+463 

101 

UB 

+13 

'.117 

-  4 

4 

146 

794 

+10 

448 

-1ft 

3 

109 

233 

14 

912 

I 

87 

147 

803 

1 

433 

1ft 

110 

103 

247 

14 

.„,- 

4 

11- 

-rj 

» 

418 

1ft 

1>U 

m 

14 

903 

1 

» 

149 

-.M 

8 

403 

1ft 

| 

105 

276 

U 

897 

a 

92 

150 

828 

8 

:i- 

1ft 

108 

106 

,"i 

U 

-Jl 

6 

151 

836 

g 

372 

18 

107 

305 

la 

--:, 

•- 

4 

152 

814 

1 

357 

15 

1 

108 

319 

u 

879 

6 

96 

153 

851 

7 

341 

1C 

105 

109 

333 

14 

-7-J 

1 

154 

858 

7 

325 

16 

14 

7 

1 

7 

It 

3 

110 

4347 

«an 

155 

+865 

+309 

111 

30 

+  14 

858 

-  7 

99 

156 

-7'J 

+  7 

293 

-1« 

102 

112 

376 

u 

851 

7 

157 

878 

< 

277 

16 

113 

390 

14 

Ml 

8 

4 

158 

-I 

6 

261 

16 

1 

114 

MM 

It 

M 

8 

103 

I.V.I 

889 

1 

245 

16 

99 

115 

418 

14 

BM 

160 

894 

1 

229 

16 

116 

M 

14 

817 

1 

161 

899 

6 

213 

16 

4 

117 

446 

14 

808 

106' 

162 

904 

I 

197 

16 

95 

118 

M 

11 

;,., 

163 

908 

4 

181 

16 

ir.i 

473 

14 

790 

1 

164 

912 

4 

164 

17 

4 

14 

10 

« 

16 

130 

+487 

+780 

106 

165 

+915 

+148 

91 

l-'l 

500 

+11 

770 

-10 

166 

918 

+  3 

132 

-18 

122 

514 

14 

7,,. 

10 

* 

167 

921 

» 

115 

17 

ft 

123 

as 

ia 

749 

11 

110 

168 

923 

3 

99 

16 

86 

124 

541 

14 

738 

11 

169 

925 

1 

83 

16 

125 

554 

IS 

727 

11 

1 

170 

927 

2 

67 

16 

ft 

126 

567 

11 

716 

11 

112 

171 

928 

1 

60 

17 

81 

127 

580 

11 

7"! 

11 

172 

929 

+  1 

34 

16 

123 

:,  •:( 

11 

I,'-:! 

11 

1 

173 

929 

0 

18 

16 

ft 

129 

606 

11 

681 

11 

113 

174 

929 

0 

+     1 

17 

76 

11 

11 

0 

16 

130 

+618 

+669 

175 

+929 

-  15 

131 

630 

+1* 

656 

-11 

-1 

176 

928 

-  1 

31 

-18 

6 

132 

643 

11 

644 

11 

114 

177 

927 

1 

47 

16 

70 

133 

G.V, 

H 

631 

11 

178 

926 

1 

63 

16 

134 

667 

11 

618 

11 

0 

179 

924 

t 

7!l 

16 

+8 

135 

..,;- 

+11 

.1,1-, 

-11 

-114 

180 

+922 

-  3 

-  95 

-16 

1,1 

58 


TABLE    IV  .—Continued. 

PEETURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  IV. 

Arg. 

& 

Diff. 

ft 

Diff. 

?1 

Diff. 

Arg. 

Ji 

Diff. 

fl 

Diff. 

tl 

Diff. 

O 

o 

180 

+922 

-  95 

-64 

225 

+481 

-700 

+38 

181 

919 

—  3 

111 

-16 

226 

465 

-16 

710 

-10 

182 

916 

3 

127 

16 

+6 

227 

450 

15 

719 

9 

+6 

183 

913 

3 

143 

16 

58 

228 

434 

16 

729 

0 

44 

184 

909 

4 

158 

15 

229 

419 

15 

738 

9 

185 

905 

4 

174 

16 

6 

230 

£03 

16 

747 

9 

6 

186 

901 

4 

190 

16 

52 

231 

387 

16 

756 

9 

50 

187 

896 

5 

205 

15 

232 

371 

16 

764 

8 

188 

891 

5 

221 

16 

7 

233 

355 

16 

773 

9 

6 

189 

885 

6 

236 

15 

45 

234 

339 

16 

781 

8 

56 

6 

15 

16 

8 

190 

+879 

-251 

235 

+323 

-789 

191 

873 

-  6 

266 

-15 

7 

236 

307 

-16 

797 

-  8 

5 

192 

866 

7 

281 

15 

38 

237 

291 

16 

805 

8 

61 

193 

859 

7 

296 

15 

238 

274 

17 

812 

7 

194 

852 

7 

311 

15 

7 

239 

258 

16 

819 

7 

5 

195 

844 

8 

326 

15 

31 

240 

242 

16 

826 

7 

66 

196 

836 

8 

340 

14 

241 

226 

16 

833 

7 

197 

828 

8 

355 

15 

• 

7 

242 

210 

16 

839 

6 

5 

198 

819 

9 

369 

14 

24 

243 

193 

17 

846 

7 

71 

199 

810 

9 

383 

14 

244 

177 

16 

652 

6 

9 

14 

7 

16 

5 

4 

200 

+801 

-397 

245 

+161 

-857 

201 

791 

-10 

411 

-14 

17 

246 

145 

-16 

863 

-  6 

75 

202 

781 

10 

425 

14 

247 

129 

16 

868 

5 

203 

771 

10 

438 

13 

7 

248 

113 

10 

873 

5 

4 

204 

760 

11 

452 

14 

10 

249 

97 

16 

878 

5 

79 

205 

749 

11 

466 

14 

250 

81 

16 

883 

5 

206 

738 

11 

479 

13 

7 

251 

65 

16 

887 

4 

207 

727 

11 

492 

13 

-  3 

252 

49 

16 

891 

4 

82 

208 

715 

12 

505 

13 

253 

34 

15 

895 

4 

209 

703 

12 

518 

13 

7 

254 

18 

16 

899 

4 

3 

13 

12 

15 

3 

210 

+691 

-530 

+  4 

255 

+    3 

-902 

85 

211 

678 

—13 

543 

-13 

256 

-  13 

-16 

905 

—  3 

212 

665 

13 

555 

12 

7 

257 

28 

15 

908 

3 

3 

213 

652 

13 

567 

12 

11 

258 

43 

15 

911 

3 

88 

214 

639 

13 

579 

12 

259 

58 

15 

913 

2 

215 

626 

13 

591 

12 

7 

260 

73 

15 

915 

2 

2 

216 

612 

14 

603 

12 

18 

261 

88 

15 

917 

2 

90 

217 

598. 

14 

614 

11 

262 

102 

14 

919 

2 

218 

584 

14 

626 

12 

7 

263 

117 

15 

920 

1 

2 

219 

570 

14 

637 

11 

25 

264 

131 

14 

921 

1 

92 

15 

11 

14 

—  1 

220 

+555 

-648 

265 

-145 

-922 

221 

541 

—14 

658 

-10 

6 

266 

160 

-15 

922 

0 

1 

222 

526 

15 

669 

11 

31 

267 

174 

14 

922 

0 

93 

223 

511 

It 

679 

10 

268 

187 

13 

922 

0 

224 

496 

15 

690 

11 

+7 

269 

201 

14 

922 

0 

+1 

225 

+481 

-15 

-700 

-10 

+38 

270 

-214 

-13 

-921 

+  1 

+94 

59 


TABLE    IV.—Gmtiim,;!. 

I'F.inTKi;  \TIn\s  ,»F  TIIF.  (  (  )-(  Mil  H  N  A  TF.S  IN  UNITS  OF  THE  SIXTH    HF.CIMAI.. 

AR<;r.\IKNT  IV. 

Arg. 

*. 

our 

fll 

itiir. 

(l 

Diff. 

An?. 

& 

Diff. 

« 

Diff. 

Cl 

Diff. 

0 

o 

270 

-214 

-921 

+94 

315 

6M 

-600 

+71 

•-'71 

M 

-14 

MO 

+  i 

316 

.,:.- 

-* 

587 

+  18 

•.'II 

11 

919 

i 

+1 

317 

664 

6 

574 

la 

-a 

273 

U 

'.M7 

9 

u 

318 

670 

6 

561 

la 

68 

'.'71 

K7 

11 

MB 

1 

319 

676 

6 

M- 

11 

••:-. 

m 

11 

013 

1 

0 

320 

t.-I 

8 

535 

11 

a 

276 

11 

'.'11 

9 

95 

321 

667 

6 

521 

u 

65 

277 

304 

19 

.„,. 

3 

322 

692 

8 

507 

u 

316 

19 

00B 

a 

-1 

323 

697 

8 

4!»3 

14 

a 

279 

m 

19 

902 

i 

94 

M 

IM 

8 

479 

u 

62 

19 

4 

8 

14 

M 

-340 

-898 

325 

-707 

-465 

•.'-1 

m 

-19 

894 

+  4 

0 

m 

712 

-9 

450 

+18 

9 

M 

:•„,:; 

11 

M 

4 

94 

327 

716 

4 

436 

14 

60 

-.'-:!            375 

11 

--., 

4 

328 

721 

9 

421 

19 

•.'-1            :'.-, 

11 

--i 

8 

1 

329 

725 

4 

406 

18 

a 

397 

11 

tn 

8 

93 

330 

729 

4 

3;  >2 

U 

57 

-.'-I,           1  1- 

11 

871 

8 

331 

733 

4 

377 

18 

-•-7 

418 

10 

MB 

6 

1 

332 

737 

4 

362 

18 

i 

M 

429 

11 

859 

6 

92 

333 

741 

4 

347 

19 

55 

289 

10 

853 

6 

334 

744 

a 

332 

14 

10 

6 

3 

4 

10 

a 

290 

-449 

-847 

335 

-748 

-316 

291 

459 

-10 

MO 

+  7 

90 

336 

751 

-8 

301 

+18 

52 

469 

10 

833 

7 

337 

754 

8 

286 

18 

293 

479 

10 

-.'•. 

8 

11 

338 

757 

a 

270 

16 

8 

294 

1- 

9 

818 

7 

88 

339 

760 

a 

255 

18 

50 

497 

9 

810 

8 

340 

762 

9 

239 

16 

296 

507 

10 

-ii-,! 

1 

1 

341 

765 

a 

223 

16 

9 

516 

9 

7.;: 

g 

86 

342 

767 

9 

208 

18 

48 

298 

524 

8 

785 

8 

343 

769 

1 

192 

16 

299 

533 

9 

776 

9 

3 

344 

771 

9 

177 

f6 

1 

9 

9 

9 

16 

300 

-542 

-767 

84 

345 

-773 

-161 

46 

Ml 

550 

-  8 

+  10 

346 

774 

-1 

145 

+  10 

302 

608 

• 

747 

10 

a 

347 

775 

1 

129 

16 

9 

303 

566 

8 

737 

10 

81 

MB 

776 

1 

114 

18 

44 

3M 

574 

8 

727 

10 

349 

777 

1 

98 

H 

305 

tea 

8 

717 

10 

a 

350 

778 

1 

82 

16 

1 

306 

590 

8 

706 

11 

79 

351 

779 

1 

66 

16 

43 

307 

607 

7 

..  •-, 

11 

352 

779 

-0 

51 

19 

308 

604 

7 

684 

II 

* 

353 

779 

0 

35 

16 

9 

309 

612 

8 

673 

II 

76 

354 

779 

9 

19 

16 

41 

7 

19 

0 

1  • 

310 

-619 

-661 

355 

-779 

-    3 

311 

626 

-  7 

649 

+11 

1 

356 

779 

0 

+  12 

+  19 

9 

312 

632 

6 

637 

19 

73 

357 

778 

+1 

24 

16 

39 

313 

630 

7 

625 

11 

358 

777 

1 

44 

16 

314 

645 

6 

613 

11 

—i 

359 

776 

1 

59 

19 

-1 

315 

-652 

' 

(,'MI 

+  18 

+71 

-775 

+1 

+  75 

+  16 

m 

60 


TABLE    IV.—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE   SIXTH   DECIMAL. 

ARGUMENT  V. 

Arg. 

& 

Diff. 

1l 

Diff. 

& 

Diff. 

Arg. 

li 

Diff. 

% 

Diff. 

& 

Diff. 

o 

o 

0 

-507 

+  52 

-  84 

135 

+358 

-188 

+150 

3 

507 

0 

39 

-13 

77 

+7 

138 

376 

+  18 

181 

+  7 

148 

-2 

6 

505 

+  2 

26 

13 

70 

7 

141 

392 

16 

174 

7 

146 

2 

JJ 

13 

16 

g 

9 

502 

+  13 

63 

7 

144 

408 

166 

144 

J 

12 

497 

5 

0 

13 

56 

7 

147 

422 

14 

158 

8 

141 

3 

15 

491 

6 

-  13 

13 

49 

7 

150 

436 

14 

150 

8 

137 

4 

18 

484 

7 

26 

13 

41 

8 

153 

448 

12 

141 

9 

133 

4 

21 

475 

9 

39 

13 

33 

8 

156 

459 

11 

132 

9 

329 

4 

24 

465 

10 

52 

13 

25 

8 

159 

469 

10 

122 

1C 

125 

4 

27 

454 

11 

64 

12 

18 

7 

162 

477 

8 

113 

9 

120 

5 

13 

13 

8 

7 

10 

5 

30 

-441 

-  77 

-  10 

165 

+484 

-103 

+115 

33 

427 

+14 

89 

-13 

-    2 

+8 

168 

490 

+  6 

92 

+  11 

109 

-6 

36 

412 

15 

100 

11 

+    6 

8 

171 

494 

4 

82 

10 

103 

6 

39' 

396 

16 

112 

12 

14 

8 

174 

497 

3 

71 

11 

97 

6 

42 

379 

17 

123 

11 

22 

8 

177 

499 

+  2 

61 

10 

91 

6 

45 

360 

19 

133 

10 

30 

8 

180 

499 

0 

50 

11 

84 

7 

48 

340 

20 

143 

10 

38 

8 

183 

498 

~  1 

39 

11 

78 

6 

51 

320 

20 

153 

10 

45 

7 

186 

496 

2 

28 

11 

71 

7 

54 

299 

21 

163 

10 

53 

8 

180 

493 

3 

16 

19 

63 

8 

57 

277 

22 

171 

8 

60 

7 

192 

488 

5 

-    5 

11 

56 

7 

23 

8 

8 

6 

11 

8 

60 

-254 

-179 

+  68 

195 

+482 

+    6 

+  48 

63 

230 

+24 

187 

-  8 

75 

+7 

198 

474 

-  8 

18 

+  12 

41 

-7 

66 

206 

24 

194 

7 

82 

7 

201 

465 

9 

29 

11 

33 

8 

69 

181 

25 

201 

7 

88 

6 

204 

455 

10 

40 

11 

25 

8 

72 

156 

25 

207 

6 

95 

7 

207 

444 

11 

51 

11 

17 

8 

75 

130 

26 

212 

5 

101 

6 

210 

432 

12 

63 

12 

9 

8 

78 

104 

26 

216 

4 

107 

6 

213 

418 

14 

74 

11 

+     1 

8 

81 

78 

26 

220 

4 

112 

5 

216 

404 

14 

84 

10 

-    7 

8 

84 

51 

27 

224 

4 

118 

6 

219 

388 

16 

95 

11 

15 

8 

87 

-  25 

•     26 

226 

2 

123 

5 

222 

371 

17 

106 

11 

23 

8 

27 

2 

4 

17 

10 

8 

90 

+    2 

-228 

+127 

225 

+354 

+116 

-  31 

93 

29 

+27 

230 

-  2 

131 

+4 

228 

335 

-19 

126 

+10 

39 

-8 

96 

55 

26 

231 

-   1 

135 

4 

231 

316 

19 

136 

10 

47 

8 

99 

81 

26 

231 

0 

139 

4 

234 

295 

21 

145 

9 

54 

7 

102 

107 

26 

230 

+  1 

142 

3 

237 

274 

21 

154 

9 

61 

7 

105 

133 

26 

229 

1 

145 

3 

240 

252 

22 

163 

9 

69 

8 

108 

159 

26 

228 

1 

147 

2 

243 

230 

22 

172 

9 

76 

7 

111 

184 

25 

226 

2 

149 

2 

246 

207 

23 

180 

8 

83 

7 

114 

208 

24 

223 

3 

151 

2 

249 

183 

24- 

187 

7 

89 

6 

117 

232 

24 

219 

4 

152 

1 

252 

.      158 

25 

194 

7 

C6 

7 

23 

4 

+  1 

25 

7 

6 

120 

+255 

-215 

+153 

255 

+133 

+201 

-102 

123 

277 

+22 

211 

+  4 

153 

0 

258- 

108 

-25 

207 

+  6 

107 

-5 

126 

298 

21 

206 

5 

153 

0 

261 

83 

25 

213 

6 

113 

6 

129 

319 

21 

200 

6 

152 

-1 

264 

57 

26 

218 

5 

118 

5 

132 

339 

20 

194 

6 

.    151 

1 

267 

31 

26 

222 

4 

123 

5 

135 

+359 

+  19 

-188 

+  6 

+150 

-1 

270 

+    5 

-26 

+226 

+  4 

-127 

-4 

61 


TABLE    IV.—  Continued. 

PEItTl  KHATIONS  OF  T1IK  ro-OKDINATKS  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  V. 

Aig.           fi          Diff. 

* 

Diff.         d          Diff. 

A*. 

t 

Diff.          i)i 

Diff.         Ci          Diff. 

o 

o 

270          +5 

+226 

-127 

315 

-351 

mi 

-149 

-  21 

+'      in 

318 

370 

-»       t0g 

147 

276              47 

M 

135 

321 

HI 

191 

145 

78 

234 

J          139 

17               j    ., 

142           ' 

98          " 

M 

1          142 

327 

420 

175 

139           ' 

124 

M 

+l          145 

330 

434 

14            166 

136           * 

149 

236 

°          147 

333 

447 

13            156 

132           4 

••M               17, 

235 

149 

336 

I.  Vi 

15           146 

10         128 

-."1             198 

m 

1          150            ' 

339 

I7.i 

11           136 

124           4 

297           222 

m 

'          151            ' 

342 

479 

125 

11         119 

• 

I                        -1 

8 

13                                  5 

300          -245 

+229 

345 

-487 

+113 

-114 

303            268        -" 

226 

M 

348 

494 

102 

109 

M 

i                            n 

• 

in                                         A 

:i  H,            290 

M 

152 

351 

499 

90 

103 

309            311 

217 

i:.l 

354 

503 

4             77 

97 

312            M 

211 

150 

357 

506 

65 

11           91 

315 

IM 

1       -149 

360 

-507 

1         +  52 

1       -84 

ARGUMENT  VI. 

Arg. 

1 

Diff. 

m 

Diff. 

frl 

A* 

Jl 

Diff. 

« 

Diff. 

& 

o 

0 

+492 

+  54 

0 

69 

+127 

+471 

3 

1" 

-  4 

79 

+»8 

72 

102 

-9* 

477 

+  8 

-4 

6 

4-:i 

5 

104 

35 

0 

75 

77 

35 

482 

5 

9 

477 

8 

129 

35 

78 

51 

36 

485 

* 

4 

12 

470 

7 

153 

34 

-1 

81 

+  25 

*• 

487 

1 

15 

461 

9 

177 

34 

84 

-    1 

* 

'    I-- 

+  1 

4 

18 

451 

10 

200 

2* 

1 

87 

27 

98 

1-7 

-  1 

21 

440 

11 

223 

3) 

90 

53 

94 

•I-:, 

1 

5 

24 

428 

13 

245 

88 

2 

93 

78 

3* 

1-J 

* 

27 

414 

14 

267 

11 

96 

104 

38 

477 

8 

5 

14 

11 

• 

35 

8 

30 

+400 

.1  •}  — 

2 

99 

-129 

+471 

33 

-1« 

MB 

+» 

102 

154 

-as 

464 

-  7 

5 

1^ 

35 

g 

36 

367 

327 

IV 

2 

105 

179 

455 

39 

349 

18 

346 

19 

108 

203 

34 

446 

9 

4 

43 

330 

19 

363 

17 

3 

111 

226 

9» 

435 

11 

45 

311 

19 

379 

18 

114 

24!t 

as 

422 

U 

4 

48 

•_»„ 

31 

395 

M 

3 

117 

271 

93 

409 

1* 

51 

960 

11 

409 

14 

120 

2-13 

93 

394 

U 

4 

54 

247 

;; 

423 

U 

3 

123 

314 

91 

379 

U 

57 

224      i 

435 

11 

126 

333 

19 

362 

17 

4 

M 

H     , 

19 

18 

60 

+201 

+446 

4 

129 

-352 

-344 

63 

177 

-M 

455 

+  9 

132 

370 

-18 

326 

-18 

4 

66 

152 

m 

464 

9 

-4 

135 

387 

17 

306 

30 

69            +127 

* 

+471 

+  7 

138 

-403 

-18 

--'' 

~* 

-3 

62 


TABLE    IV  .—Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  VI. 

Atg. 

Si 

Diff. 

•ni 

Diff. 

Si 

Arg. 

Si 

Diff. 

% 

Diff. 

£l 

o 
138 

-403 

+286 

-3 

o 
249 

-125 

-473 

141 

418 

-16 

265 

-21 

252 

100 

+25 

479 

-  6 

+4 

145 

431 

13 

243 

22 

3 

255 

74 

26 

483 

4 

147 

444 

13 

220 

23 

258 

48 

26 

486 

3 

4 

1  J 

23 

26 

150 

455 

197 

3 

261 

-  22 

488 

J, 

153 

465 

10 

173 

24 

264 

+    4 

26 

488 

0 

5 

156 

474 

9 

149 

24 

2 

267 

30 

26 

487 

+  1 

159 

481 

7 

124 

25 

270 

56 

26 

485 

2 

5 

163 

487 

6 

99 

25 

2 

273 

81 

25 

481 

4 

165 

492 

5 

74 

25 

276 

107 

26 

476 

5 

5 

3 

26 

25 

6 

168 

-495 

+  48 

1 

279 

+132 

-470 

171 

497 

-  2 

+  23 

-25 

282 

157 

+25 

462 

+  8 

5 

174 

498 

-  1 

-    3 

26 

-1 

285 

181 

24 

453 

9 

177 

497 

+  1 

29 

26 

288 

205 

24 

443 

10 

5 

180 

495 

2 

54 

25 

0 

291 

228 

23 

432 

11 

183 

491 

4 

80 

26 

294 

251 

23 

420 

12 

4 

186 

486 

5 

105 

25 

'o 

297 

273 

22 

406 

14 

189 

480 

6 

130 

25 

300 

294 

21 

391 

15 

4 

192 

472 

8 

155 

25 

+1 

303 

314 

20 

376 

15 

195 

464 

8 

179 

24 

306 

334* 

20 

359 

17 

4 

10 

23 

19 

18 

198 

-454 

-202 

1 

309 

+353 

-341 

201 

442 

+12 

225 

-23 

312 

370 

+17 

323 

+18 

4 

204 

430 

12 

248 

23 

2 

315 

387 

17 

303 

20 

207 

416 

14 

270 

22 

318 

402 

15 

283 

20 

3 

210 

401 

15 

291 

21 

2 

321 

417 

15 

262 

21 

213 

385 

16 

311 

20 

324 

430 

13 

240 

22 

3 

216 

368 

17 

330 

19 

2 

327 

442 

12 

217 

23 

219 

349 

19 

349 

19 

330 

453 

11 

194 

23 

3 

222 

330 

19 

366 

17 

3 

333 

463 

10 

171 

23 

225 

310 

20 

383 

17 

336 

472 

9 

147 

24 

2 

20 

15 

7 

25 

228 

-290 

-398 

•3 

339 

+479 

-132 

231 

268 

+22 

412 

-14 

342 

4a5 

+  6 

98 

+24 

2 

234 

246 

23 

426 

14 

4 

345 

489 

4 

73 

25 

237 

223 

23 

438 

12 

348 

492 

3 

47 

26 

1 

240 

199 

24 

448 

10 

4 

351 

494 

2 

-  22 

25 

243 

175 

24 

458 

10 

354 

495 

+  1 

+    3 

25 

•    +1 

246 

150 

25 

466 

8 

+4 

357 

494 

-  1 

29 

26 

249   . 

-125 

+25 

-473 

-  7 

360 

+492 

-  2 

+  54 

+25 

0 

• 

TABLE    IV.—  Continued, 

1-i.ini  ur-  vriiixs  OF  TIIK  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  VIL 

A*. 

t 

Diff. 

1l 

Diff. 

& 

Ai* 

6 

Diff. 

«»1 

Diff. 

fl 

o 

0 

0 

-231 

•    4 

-20 

135 

+292 

MO 

3 

~  ' 

8 

~ 

138 

322 

+10 

tea 

+17 

+  8 

.. 

M 

1 

13 

21 

141 

350 

• 

364 

19 

9 

-.".I 

i 

18 

144 

377 

97 

342 

91 

10 

19 

m 

i 

23 

22 

147 

403 

M 

319 

91 

15 

m 

1 

29 

150 

426 

91 

203 

M 

13 

18 

240 

i 

35 

23 

153 

448 

99 

266 

«7 

• 

243 

i 

42 

156 

MB 

90 

216 

10 

u 

24 

9 

GO 

2-1 

159 

485 

17 

n 

11 

27 

•Jl- 

1 

58 

162 

500 

II 

173 

19 

16 

9 

1 

11 

U 

30 

-250 

-67 

24 

165 

+r,13 

-140 

33 

-  I 

77 

-10 

168 

M 

+  » 

106 

+M 

1* 

36 

255 

9 

88 

n 

24 

171 

520 

7 

70 

M 

39 

256 

1 

99 

11 

174 

533 

4 

-  35 

U 

10 

49 

258 

-  3 

112 

11 

23 

177 

534 

+  1 

+    1 

M 

45 

m 

0 

126 

M 

180 

533 

-  1 

37 

M 

20 

48 

M 

0 

140 

14 

23 

183 

528 

t 

72 

a 

51 

n 

0 

155 

It 

186 

521 

7 

107 

u 

21 

54 

256 

+  a 

171 

18 

22 

l-'.i 

511 

10 

142 

U 

57 

253 

.1 

187 

10 

192 

498 

11 

175 

.: 

*J 

4 

n 

1« 

19 

60 

-249 

-204 

21 

195 

-  I-J 

+207 

63 

244 

+  6 

222 

-18 

198 

464 

-18 

238 

+11 

22 

66 

237 

7 

230 

17 

10 

201 

444 

90 

267 

99 

69 

229 

8 

257 

18 

204 

422 

29 

2!t4 

97 

23 

72 

220 

9 

275 

18 

18 

207 

398 

94 

320 

9« 

75 

IOB 

11 

203 

18 

210 

372 

M 

343 

91 

23 

78 

196 

11 

311 

ia 

16 

213 

345 

97 

364 

91 

81 

182 

U 

328 

n 

216 

316 

99 

383 

19 

22 

84 

166 

18 

345 

n 

14 

219 

•.'-«. 

M 

400 

17 

87 

149 

17 

362 

17 

222 

M 

M 

414 

14 

22 

• 

ia 

11 

11 

90 

-129 

-377 

12 

225 

+225 

+425 

93 

109 

+90 

391 

-14 

228 

194 

-11 

434 

+  9 

21 

96 

88 

91 

404 

11 

9 

231 

162 

39 

441 

1 

99 

62 

:i 

416 

19 

234 

131 

11 

445 

4 

20 

102 

37 

15 

426 

10 

1 

237 

100 

11 

447 

+  9 

!»:, 

-  10 

47 

434 

8 

240 

69 

11 

447 

0 

10 

108 

+  18 

98 

441 

7 

4 

243 

40 

99 

444 

-  1 

111 

47 

99 

445 

4 

246 

+  11 

99 

440 

4 

18 

114 

76 

99 

448 

-  1 

-  2 

2-10 

-  17 

98 

433 

7 

117 

107 

11 

448 

0 

252 

44 

« 

424 

9 

17 

11 

+  1 

• 

10 

120 

+138 

-446 

+  1 

255 

-  69 

+414 

123 

169 

+11 

442 

+  4 

258 

93 

-94 

402 

-19 

15 

126 

200 

11 

435 

7 

3 

261 

li:. 

99 

389 

11 

129 

231 

11 

426 

1 

264 

136 

91 

375 

14 

13 

132 

262 

11 

414 

19 

+  6 

267 

155 

19 

360 

M 

135 

+202 

+» 

-400 

+14 

270 

-172 

-n 

+344 

-w 

+11 

64 


TABLE    IV.  —  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE   SIXTH   DECIMAL. 

ARGUMENT  VII. 

Arg. 

?! 

.Diff. 

* 

Diff. 

Ek 

Arg. 

li 

Diff. 

* 

Diff. 

& 

o 

o 

270 

-172 

+344 

+11 

315 

-259 

+100 

273 

188 

-16 

327 

-17 

318 

257 

+2 

88 

-12 

-  7 

276 

202 

14 

309 

IS 

9 

321 

255 

2 

78 

10 

279 

214 

12 

2!)2 

17 

324 

252 

3 

68 

10 

9 

282 

225 

11 

274 

18 

7 

327 

249 

3 

59 

9 

285 

234 

9 

256 

18 

330 

247 

2 

51 

8 

11 

288 

242 

8 

238 

18 

5 

333 

244 

3 

43 

8 

291 

248 

6 

220 

18 

336 

241 

3 

36 

7 

13 

294 

253 

5 

203 

17 

+  3 

339 

239 

2 

30 

6 

297 

257 

4 

186 

n 

342 

237 

2 

24 

6 

15 

3 

16 

2 

5 

300 

-260 

+170 

0 

345 

-235 

+  19 

303 

261 

-  I 

155 

-15 

348 

233 

+2 

14 

5 

17 

306 

262 

-  I 

140 

15 

-  2 

351 

232 

1 

9 

6 

309 

262 

0 

126 

14 

354 

231 

+1 

5 

4 

19 

312 

261 

+  1 

112 

14 

-  4 

357 

231 

0 

+     1 

4 

315 

-259 

+  2 

+100 

-12 

360 

-231 

0 

-     4 

-  5 

-20 

ARGUMENT  VIII. 

Arg. 

li 

Diff. 

m 

Diff. 

& 

Arg. 

ft 

Diff. 

rn 

Diff. 

fl 

o 

0 

-352 

+  22 

-7 

69 

-106 

+335 

3 

350 

+  2 

40 

+18 

72 

88 

+18 

340 

+  5 

+  6 

JJ 

18 

18 

^ 

6 

347 

58 

6 

75 

70 

344 

9 

344 

3 

76 

18 

78 

52 

is' 

347 

3 

7 

e 

Ifi 

18 

2 

12 

339 

94 

lo 

5 

81 

34 

349 

15 

334 

6 

112 

18 

84 

-  15 

19 

350 

1 

8 

18 

328 

6 

129 

17 

4 

87 

+    3 

18 

351 

+  ! 

21 

320 

8 

146 

17 

90 

22 

•      19 

350 

-  1 

9 

a 

18 

• 

24 

312 

163 

3 

93 

40 

348 

27 

303 

9 

179 

16 

96 

58 

18 

346 

2 

9 

9 

15 

18 

4 

30 

-294 

+194 

2 

99 

+  76 

+342 

33 

283 

+11 

209 

+15 

102 

94 

+18 

338 

-  4 

10 

36 

272 

11 

224 

15 

-1 

105 

112 

18 

332 

6 

39 

260 

12 

238 

14 

108 

129 

17 

326 

6 

10 

42 

247 

13 

251 

13 

0 

111 

146 

17 

319 

7 

45 

233 

14 

263 

12 

114 

162 

16 

311 

8 

11 

14 

12 

16 

Q 

48 

219 

275 

+2 

117 

178 

302 

51 

204 

15 

286 

n 

120 

194 

16 

292 

10 

11 

54 

189 

15 

296 

10 

3 

123 

209 

15 

281 

11 

57 

173 

16 

306 

10 

126 

224 

15 

270 

11 

11 

16 

8 

14 

12 

60 

-157 

+314 

4 

129 

+238 

+258 

63 

140 

+17 

322 

_+  8 

132 

251 

+13 

245 

-13 

11 

66 

123 

17 

329 

7 

+5 

135 

263 

12 

232 

13 

69 

-106 

+17 

+335 

+  6 

138 

+275 

+12 

+218 

-14 

+11 

TABLE    IV.—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATI.^  IX  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  VIII 

Arg. 

fc 

Diff. 

I, 

Diff. 

Ci 

A*. 

{, 

Diff. 

ll 

Diff. 

Ci 

Q 

o 

--'?". 

+218 

+11 

249 

+106 

-335 

-  6 

141 

•J-<, 

+11 

Ml 

-is 

252 

89 

-17 

340 

-  s 

144 

M 

n 

188 

i> 

11 

MB 

71 

18 

344 

4 

7 

147 

306 

9 

172 

18 

258 

53 

18 

347 

S 

BU 

9 

l  .. 

18 

11 

261 

34 

n 

349 

1 

a 

ID 

322 

7 

139 

n 

264 

+  16 

18 

350 

1 

IM 

MI 

7 

122 

17 

10 

267 

-    3 

19 

351 

—  1 

9 

IflB 

MB 

8 

105 

17 

270 

21 

18 

350 

+  1 

162 

340 

» 

87 

18 

9 

273 

39 

18 

349 

1 

9 

165 

344 

4 

69 

18 

276 

58 

19 

346 

S 

4 

18 

18 

4 

168 

+348 

+  51 

9 

279 

-  76 

-342 

10 

171 

NQ 

+  1 

33 

-18 

-.'--' 

94 

-18 

338 

+  4 

171 

351 

1 

+  15 

18 

8 

285 

111 

n 

333 

1 

10 

177 

352 

+  1 

-    3 

18 

288 

129 

18 

323 

7 

180 

-  1 

22 

19 

7 

291 

146 

n 

319 

7 

11 

183 

349 

1 

40 

18 

2)4 

162 

18 

311 

8 

186 

347 

2 

66 

18 

6 

2)7 

178 

18 

302 

9 

11 

189 

343 

4 

76 

18 

300 

194 

18 

2)2 

10 

192 

339 

4 

94 

18 

5 

303 

209 

IS 

282 

10 

11 

195 

334 

S 

112 

18 

306 

224 

IS 

271 

11 

7 

17 

14 

11 

196 
901 

+327 
MB 

-     7 

-129 
146 

-17 

4 

309 
312 

-238 
251 

-IS 

-259 
246 

+1S 

11 

'.Ml 

312 

8 

162 

18 

3 

315 

264 

IS 

232 

14 

11 

207 

303 

9 

178 

18 

318 

276 

13 

218 

14 

S10 

•_"l 

9 

194 

18 

2 

321 

•J-7 

11 

203 

IS 

11 

213 

MB 

11 

209 

IS 

324 

297 

10 

1-- 

IS 

216 

n 

11 

MB 

14 

+  1 

327 

306 

9 

173 

IS 

11 

•Jl  > 

MB 

11 

237 

14 

330 

315 

9 

156 

17 

222 

247 

13 

250 

IS 

0 

333 

323 

8 

140 

18 

10 

225 

233 

14 

263 

IS 

336 

330 

7 

123 

17 

14 

13 

8 

18 

MB 

+21!) 

HBM 

-  2 

339 

-336 

-105 

9 

231 

905 

-14 

286 

-11 

342 

341 

-  S 

87 

+  18 

234 

MB 

18 

2)6 

10 

3 

345 

345 

4 

70 

17 

9 

237 

173 

18 

305 

9 

348 

MB 

S 

51 

19 

240 

157 

18 

314 

9 

4 

351 

351 

S 

33 

18 

8 

243 

141 

18 

322 

8 

354 

352 

-  1 

-  15 

18 

M6 

194 

n 

329 

7 

-  5 

357 

BBi 

0 

+    4 

19 

+  7 

M9 

+106 

-M 

-M6 

-  * 

360 

-MB 

0 

-4  •---' 

+IS 

66 


TABLE    IV.  —  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  IX. 

Arg. 

& 

Diff. 

* 

Diff. 

?! 

Arg. 

li 

Diff. 

111 

Diff. 

tl 

o 
0 

+150 

-    3 

+22 

o 

180 

-305 

+  3 

+  11 

+34 

-24 

5 

150 

0 

11 

~~  8 

20 

185 

302 

45 

21 

10 

150 

0 

18 

7 

18 

190 

294 

8 

78 

33 

19 

15 

151 

+  i 

26 

8 

16 

195 

282 

12 

110 

32 

16 

20 

152 

i 

34 

8 

13 

200 

267 

15 

140 

30 

13 

25 

153 

+  i 

43 

9 

11 

205 

247 

20 

167 

27 

10 

30 

153 

0 

53 

10 

8 

210 

225 

22 

192 

25 

7 

35 

153 

0 

63 

10 

6 

215 

200 

25 

212 

20 

•4 

40 

153 

0 

75 

12 

+  3 

220 

172 

28 

230 

18 

-  1 

45 

152 

-  1 

87 

12 

0 

225 

144 

28 

243 

13 

+  2 

3 

13 

29 

9 

50 
55 

+149 
146 

-3 

-100 
114 

-14 

-  2 

5 

230 
235 

-115 

86 

+29 

+252 
257 

+  5 

+  5 

8 

60 

141 

6 

128 

14 

8 

240 

57 

29 

259 

+  2 

11 

65 

134 

7 

143 

15 

10 

245 

29 

28 

257 

—  2 

13 

70 

126 

8 

158 

15 

13 

250 

-    3 

26 

252 

6 

16 

75 

116 

10 

173 

15 

16 

255 

+  22 

25 

244 

8 

18 

80 

104 

12 

188 

15 

18 

260 

45 

23 

234 

10 

21 

85 

89 

15 

202 

14 

20 

265 

65 

20 

222 

12 

23 

90 

72 

17 

216 

14 

23 

270 

83 

18 

209 

13 

25 

95 

53 

19 

228 

12 

25 

275 

99 

16 

194 

15 

26 

22 

10 

14 

16 

100 

+  31 

-238 

-27 

280 

+113 

+178 

+28 

105 

+    7 

-24 

246 

-  8 

28 

285 

.  124 

+11 

163 

—15 

29 

110 

-  18 

25 

252 

6 

30 

290 

132 

8 

147 

16 

30 

115 

45 

27 

255 

-  3 

31 

295 

139 

7 

131 

16 

31 

120 

73 

28 

255 

0 

32 

300 

144 

6 

116 

15 

31 

125 

101 

28 

251 

+  4 

33 

305 

148 

4 

102 

14 

32 

130 

130 

29 

243 

8 

34 

310 

150 

2 

89 

13 

32 

135 

159 

29 

232 

11 

34 

315 

152 

+  2 

76 

13 

32 

140 

186 

27 

217 

15 

34 

320 

152 

0 

64 

12 

31 

145 

212 

26 

198 

19 

34 

325 

152 

0 

54 

10 

31 

24 

2S 

0 

10 

150 

-236 

-176 

-33 

330 

+152 

+  44 

+30 

155 

257 

-21 

150 

+26 

32 

335 

151 

-  1 

35 

—  9 

29 

160 

274 

17 

121 

29 

31 

340 

150 

1 

27 

8 

28 

165 

288 

14 

90 

31 

29 

345 

150 

0 

19 

8 

27 

170 

298 

10 

58 

32 

28 

350 

150 

0 

11 

8 

25 

175 

304 

6 

-  24 

34 

26 

355 

149 

-  1 

+    4 

7 

24 

180 

-305 

-  1 

+  11 

+86 

-24 

360 

+150 

+  1 

-    3 

-  7 

+22 

tt 


TABLE    IV  .—Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH   DECIMAL. 

ARGUMENT  X 

Arg. 

ft 

Diff. 

ft 

Diir. 

Arg. 

6 

Diff. 

1l 

Diff. 

& 

o 

0 

0 

+187 

-  10 

+  6 

1-0 

-178 

+  17 

-  6 

5 

186 

-  l 

26 

-w 

5 

185 

175 

+  i 

33 

+l« 

5 

10 

183 

I 

43 

17 

4 

190 

171 

4 

48 

16 

4 

15 

178 

4 

60 

n 

3 

195 

166 

5 

62 

14 

:t 

20 

ITS 

« 

76 

18 

3 

200 

159 

1 

76 

14 

2 

25 

164 

8 

91 

H 

2 

205 

152 

7 

90 

14 

I 

30 

155 

» 

1(16 

19 

+  1 

210 

143 

1 

103 

13 

_  | 

35 

145 

10 

120 

14 

0 

215 

134 

» 

115 

13 

0 

40 

133 

19 

133 

13 

-  1 

220 

123 

11 

126 

11 

+  1 

1. 

121 

13 

145 

12 

2 

225 

112 

11 

136 

10 

1 

14 

11 

H 

10 

50 

+107 

-156 

-  3 

230 

-100 

+146 

+  3 

58 

92 

-14 

165 

-  » 

4 

235 

87 

+11 

l.r>4 

+  8 

4 

60 

77 

IS 

173 

8 

5 

240 

74 

n 

162 

8 

5 

65 

61 

Id 

l-n 

7 

6 

245 

60 

14 

168 

a 

6 

TO 

45 

H 

1-:, 

ft 

7 

250 

46 

14 

173 

4 

6 

75 

28 

17 

1-- 

1 

7 

255 

32 

14 

177 

4 

7 

80 

+  11 

17 

190 

9 

8 

HO 

17 

15 

180 

1 

8 

85 

-    6 

17 

m 

-  1 

9 

265 

-    2 

It 

181 

1 

8 

90 

23 

17 

i-  • 

+  a 

9 

270 

+  14 

la 

182 

+  1 

0 

• 

39 

19 

187 

a 

10 

275 

29 

15 

180 

-  9 

9 

16 

4 

15 

9 

100 

-  55 

-183 

-10 

280 

+  44 

+178 

+10 

105 

71 

-1« 

177 

+  » 

10 

285 

59 

+  14 

174 

-  4 

in 

110 

86 

H 

170 

7 

11 

290 

73 

14 

16!) 

5 

11 

118 

100 

14 

162 

8 

11 

295 

87 

14 

163 

6 

11 

120 

113            " 

in 

10 

11 

300 

101 

14 

156 

11 

125 

125 

13 

141 

11 

11 

305 

114 

13 

147 

11 

130 

136 

11 

130 

11 

11 

310 

126 

19 

137 

10 

11 

136 

146 

10 

117 

13 

11 

315 

138 

19 

126 

11 

11 

140 

155 

« 

104 

13 

10 

320 

148 

10 

114 

13 

11 

145 

163 

8 

90 

14 

10 

325 

158 

10 

101 

11 

in 

« 

u 

8 

14 

150 

-169 

-  75 

-10 

330 

+166 

+  87 

+10 

155 

174 

-  5 

60 

+15 

9 

335 

173 

+  7 

72 

-14 

9 

169 

177 

1 

45 

U 

9 

340 

179 

• 

67 

15 

9 

Ml 

179 

3 

29 

M 

8 

345 

183 

4 

41 

M 

8 

170 

180 

-  1 

-  14 

15 

7 

350 

186 

> 

24 

17 

8 

175 

180 

0 

+    2 

H 

7 

355 

187 

+   1 

+    7 

17 

7 

180 

-178 

+  1 

-    17 

•Mi 

-  6 

no 

-1-7 

0 

1<> 

-17 

+  6 

ft 

68 


TABLE    IV.—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  XI. 

Arg. 

Ji 

Diff. 

1)1 

Diff. 

fc 

Arg. 

b 

Diff. 

* 

Diff. 

Si 

o 

o 

0 

+101 

+  11 

-  3 

180 

-144 

+  10 

-30 

5 

98 

-  3 

30 

+19 

-  1 

185 

144 

0 

8 

-  2 

31 

10 

92 

6 

48 

18 

+  1 

190 

144 

0 

6 

2 

31 

15 

83 

9 

65 

17 

2 

195 

145 

-  1 

+    3 

3 

32 

14 

A 

3 

20 

72 

a 

79 

3 

200 

145 

0 

32 

25 

58 

14 

92 

13 

4 

205 

145 

0 

-    3 

3 

33 

30 

43 

15 

102 

10 

4 

210 

146 

-  1 

6 

3 

34 

35 

27 

16 

110 

8 

4 

215 

146 

0 

10 

4 

34 

40 

+  11 

16 

116 

6 

4 

220 

146 

0 

14 

4 

35 

Ifl 

g 

A 

45 

-    5 

10 

119 

3 

225 

146 

18 

36 

16 

+  i 

+  1 

5 

50 

-  21 

+120 

+  2 

230 

-145 

-  23 

-36 

55 

36 

-15 

119 

-  i 

+  1 

235 

144 

+  1 

28 

-  5 

37 

60 

51 

15 

117 

2 

0 

240 

142 

2 

34 

6 

37 

65 

64 

13 

114 

3 

-  2 

245 

140 

2 

41 

7 

37 

70 

76 

12 

110 

4 

3 

250 

137 

3 

47 

6 

38 

75 

87 

11 

105 

6 

5 

255 

133 

4 

54 

7 

38 

80 

97 

10 

99 

6 

7 

260 

128 

5 

61 

7 

38 

85 

106 

9 

93 

6 

9 

265 

122 

6 

69 

8 

38 

90 

113 

7 

86 

7 

10 

270 

115 

7 

76 

7 

38 

95 

120 

7 

80 

6 

12 

275 

106 

9 

83 

7 

37 

5 

7 

9 

7 

100 

-125 

+  73 

-14 

280 

-  97 

-  90 

-37 

—  •  6 

+1  1 

105 

130 

0 

67 

15 

285 

86 

—11 

96 

36 

110 

133 

3 

61 

6 

17 

290 

74 

12 

101 

5 

35 

115 

136 

3 

55 

6 

18 

295 

60 

14 

106 

5 

34 

120 

139 

3      . 

49 

6 

19 

300 

46 

14 

109 

3 

32 

125 

140 

1 

44 

5 

21 

305 

30 

16 

111 

-  2 

30 

130 

141 

1 

40 

4 

22 

310 

-  13 

17 

111 

0 

28 

135 

142 

1 

36 

4 

23 

315 

+    4 

17 

108 

+  3 

26 

140 

143 

1 

32 

4 

24 

320 

21 

17 

103 

5 

24 

145 

143 

0   • 

29 

3 

25 

325 

38 

17 

96 

7 

21 

0 

3 

16 

9 

150 

-143 

+  26 

-26 

330 

+  54 

-  87 

-19 

155 

143 

-  o 

23 

-  3 

26 

335 

68 

+14 

75 

+12 

16 

160 

143 

0 

20 

3 

27 

340 

80 

12 

60 

15 

13 

165 

143 

0 

18 

2 

28 

345 

90 

10 

44 

16 

10 

170 

143 

0 

15 

3 

29 

350 

97 

7 

26 

18 

8 

175 

144 

-  1 

13 

2 

29 

355 

101 

+  4 

-    7 

19 

5 

180 

-144 

0 

+  10 

-  s 

-30 

360 

+101 

0 

+  11 

+18 

-  3 

• 

* 

TABLE    IV  .—Continued. 

Pl.lMl  UBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  XIL 

Arg. 

fc 

Diff. 

« 

Diff. 

b 

Arg. 

fc 

Diff. 

* 

Diff. 

Q 

o 

o 

0 

-  97 

-    6 

-2 

ISO 

+132 

+    8 

+3 

5 

96 

+  i 

13 

-  7 

185 

130 

-   !l 

30 

+u 

10 

95 

i 

21 

8 

2 

190 

117 

31 

n 

2 

i:. 

94 

i 

38 

7 

195 

114 

43 

11 

20 

93 

3 

35 

7 

3 

200 

109 

53 

10 

3 

•j-, 

gg 

a 

43 

8 

M 

103 

63 

10 

30 

86 

a 

50 

7 

3 

210 

96 

71 

9 

3 

83 

4 

67 

7 

315 

88 

8 

79 

8 

40 

78 

4 

64 

7 

2 

220 

80 

8 

86 

7 

2 

45 

74 

4 

70 

1 

225 

71 

9 

93 

7 

e 

7 

10 

6 

50 

-68 

-  77 

2 

230 

+  61 

+  98 

2 

55 

63 

+  « 

83 

— 

235 

51 

-10 

103 

+  4 

61) 

56 

• 

88 

2 

340 

41 

10 

106 

a 

3 

65 

49 

7 

93 

245 

31 

10 

109 

a 

70 

41 

8 

98. 

2 

250 

20 

11 

110 

i 

2 

Q 

10 

*  | 

33 

102 

255 

+  10 

111 

80 

34 

9 

I,.:, 

1 

260 

0 

10 

110 

-  i 

1 

85 

15 

9 

108 

265 

-  10 

10 

109 

i 

90 

-    5 

10 

109 

1 

270 

19 

9 

107 

9 

1 

10 

• 

M 

+    5 

110 

275 

39 

104 

10 

0 

8 

4 

100 

+  15 

-110 

-1 

280 

-  37 

+100 

+1 

1".-, 

35 

+10 

109 

+  1 

385 

45 

-  8 

96 

-  4 

110 

36 

11 

107 

9 

0 

390 

53 

8 

91 

* 

0 

11.-, 

46 

10 

105 

9 

395 

60 

7 

86 

1 

m 

56 

10 

101 

4 

0 

300 

66 

a 

80 

a 

0 

135 

66 

10 

96 

6 

305 

73 

' 

74 

' 

130 

75 

9 

90 

A 

+1 

310 

77 

s 

67 

7 

-1 

UB 

84 

9 

83 

7 

315 

81 

4 

60 

7 

140 

93 

8 

75 

8 

1 

320 

85 

4 

53 

7 

1 

145 

99 

7 

66 

9 

325 

88 

a 

46 

7 

7 

9 

a 

7 

150 

+106 

-  57 

1 

330 

-  91 

+  39 

1 

155 

111 

+  I 

47 

+10 

335 

93 

-  9 

32 

-  7 

160 

lir, 

4 

37 

10 

2 

340 

95 

3 

34 

8 

2 

165 

119 

4 

36 

11 

345 

96 

1 

17 

7 

170 

121 

9 

15 

11 

2 

350 

97 

-  1 

0 

8 

2 

175 

122 

+  1 

-    3 

11 

355 

97 

0 

+    3 

7 

1-d 

0 

+    8 

+11 

+3 

360 

-  97 

0 

-    6 

-  8 

-3 

i 

70 


* 

TABLE    IN  .—Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  XIII. 

Arg. 

ii 

Diff. 

* 

Diff. 

fl 

Arg. 

Ji 

Diff. 

4k 

Diff. 

Si 

o 

o 

0 

-83 

0 

-  6 

180 

+83 

+  0 

+  6 

5 

82 

+1 

-  4 

-4 

185 

82 

-i 

3 

+3 

10 

80 

3 

7 

3 

4 

190 

80 

2 

7 

4 

4 

15 

78 

2 

11 

4 

195 

78 

2 

10 

3 

20 

75 

3 

14 

3 

-  2 

200 

75 

3 

14 

4 

+  2 

25 

72 

3 

17 

3 

205 

71 

4 

17 

3 

30 

68 

4 

21 

4 

0 

210 

67 

4 

20 

3 

0 

35 

63 

5 

24 

3 

215 

62 

6 

23 

3 

40 

58 

5 

26 

2 

+  1 

220 

57 

5 

26 

3 

-  1 

45 

52 

6 

29 

3 

225 

52 

5 

28 

2 

6 

2 

6 

3 

50 

-46 

-31 

3 

230 

+46 

+31 

3 

55 

40 

+6 

33 

-2 

235 

39 

-7 

33 

+2 

60 

33 

7 

35 

2 

5 

240 

33 

6 

35 

2 

5 

65 

26 

7 

37 

2 

245 

26 

7 

36 

1 

70 

19 

7 

38 

1 

7 

250 

19 

7 

38 

2 

7 

75 

12 

7 

39 

1 

255 

12 

7 

39 

1 

80 

-  5 

7 

40 

-1 

8 

260 

+  5 

7 

40 

+1 

8 

85 

+  3 

8 

40 

0 

265 

-  3 

8 

40 

0 

90 

10 

7 

40 

0 

9 

270 

10 

7 

40 

0 

9 

95 

17 

7 

40 

0 

275 

17 

7 

40 

0 

7 

+1 

7 

0 

100 

+24 

-39 

10 

280 

-24 

+40 

10 

105 

31 

+7 

39 

+0 

285 

31 

-7 

39 

-1 

110 

38 

7 

39 

1 

10 

290 

38 

7 

38 

1 

10 

115 

44 

6 

36 

2 

295 

44 

6 

37 

1 

120 

50 

6 

34 

2 

11 

300 

50 

6 

35 

2 

11 

125 

56 

6 

32 

2 

305 

56 

6 

33 

2 

130 

61 

5 

30 

2 

11 

310 

61 

5 

31 

2 

11 

135 

66 

6 

28 

2 

315 

66 

6 

29 

2 

140 

70 

4 

25 

3 

10 

320 

70 

4 

26 

3 

10 

145 

74 

4 

23 

2 

325 

74 

4 

23 

3 

3 

3 

3 

3 

150 

+77 

-20 

9 

330 

-77 

+20 

9 

155 

80 

+3 

17 

+3 

335 

80 

-3 

17 

-3 

160 

82 

2 

13 

4 

8 

340 

82 

2 

14 

3 

8 

165 

83 

1 

10 

3 

345 

83 

1 

10 

4 

170 

84 

+1 

7 

3 

7 

350 

84 

-1 

7 

3 

7 

175 

84 

0 

-  3 

4 

355 

84 

0 

+  3 

4 

180 

+83 

-1 

0 

+3 

+  6 

360 

-«3 

+1 

0 

-3 

-  6 

TABLE    IV.—Gmlimud. 

I'KUri  Kl'.ATIONS  OF  THE  CO-ORD1.VVI  KS   IN   INITS  OF  TIIK   SIXTH    1>I.<  IMAL. 

ARGUMKNT  XIV. 

An: 

fi 

Diff. 

fli 

Diff. 

b 

AIR. 

fl 

Diff. 

« 

Diff. 

fi 

o 

0 

+44 

+  3 

tt 

I  -u 

-54 

-  2 

-2 

5 

•i:. 

41 

-  1 

—4 

165 

64 

0 

4  3 

4» 

10 

45 

0 

4 

3 

2 

190 

64 

0 

8 

ft 

2 

u 

44 

-i 

7 

3 

M 

63 

+1 

13 

30 

44 

0 

11 

4 

1 

200 

51 

9 

18 

1 

43 

i 

14 

3 

Ml 

49 

9 

23 

30 

4-.' 

1 

18 

4 

+1 

210 

47 

9 

27 

-1 

:tr, 

41 

i 

21 

I 

215 

44 

' 

31 

40 

3:  i 

9 

34 

3 

0 

M 

40 

4 

35 

0 

45 

37 

9 

38 

4 

225 

37 

a 

38 

a 

9 

3 

4 

a 

50 

-t;iT, 

-31 

-1 

230 

-33 

+41 

+1 

.V, 

33 

-3 

34 

~* 

235 

29 

+4 

44 

+* 

60 

30 

9 

37 

3 

1 

240 

24 

1 

46 

9 

1 

27 

3 

40 

3 

245 

20 

4 

47 

1 

TO 

23 

4 

42 

9 

2 

350 

15 

1 

48 

1 

2 

n 

20 

3 

44 

9 

255 

11 

4 

49 

1 

80 

16 

4 

46 

9 

2 

260 

6 

i 

60 

+  1 

2 

85 

12 

4 

48 

9 

365 

-  2 

4 

49 

-I 

90 

8 

4 

49 

1 

3 

270 

+  2 

4 

49 

0 

3 

Be 

+  3 

8 

50 

1 

275 

7 

1 

48 

1 

4 

-1 

4 

1 

100 

_  i 

—51 

3 

•_>-!  1 

+11 

+47 

3 

105 

6 

~* 

61 

0 

385 

14 

43 

45 

-9 

110 

11 

6 

51 

0 

3 

390 

18 

4 

44 

1 

3 

in 

15 

4 

50 

+1 

395 

22 

4 

42 

9 

130 

20 

* 

49 

1 

3 

300 

25 

3 

39 

3 

3 

at 

25 

1 

47 

9 

305 

28 

3 

37 

2 

130 

39 

4 

45 

9 

4 

310 

30 

9 

34 

3 

4 

i:Ci 

33 

4 

42 

3 

315 

33 

a 

31 

a 

140 

37 

4 

39 

a 

3 

320 

35 

9 

28 

a 

3 

145 

41 

4 

35 

4 

325 

37 

2 

25 

a 

a 

4 

2 

3 

150 

-44 

-31 

3 

330 

+39 

+22 

3 

l.V, 

47 

~* 

27 

+4 

335 

40 

+1 

19 

-a 

160 

60 

* 

23 

4 

3 

340 

42 

2 

16 

3 

3 

165 

53 

9 

18 

5 

345 

43 

1 

13 

3 

170 

53 

1 

13 

1 

3 

350 

43 

0 

10 

3 

3 

175 

64 

-1 

8 

4 

355 

44 

+  1 

6 

4 

I-" 

M 

0 

-2 

+0 

-8 

360 

+44 

0 

+  3 

-a 

48 

TABLE    IV.  —  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  XV. 

Arg. 

li 

Diff. 

« 

Diff. 

& 

Arg. 

li 

Diff. 

* 

Diff. 

fl 

o 

o 

0 

-29 

_  2 

0 

180 

+31 

+  2 

0 

5 

29 

0 

4 

-2 

0 

185 

31 

0 

5 

+3 

0 

10 

29 

0 

7 

3 

0 

190 

30 

-1 

7 

o 

0 

15 

28 

+1 

9 

2 

0 

195 

29 

1 

10 

3 

0 

20 

27 

1 

12 

3 

0 

200 

28 

1 

13 

3 

0 

25 

26 

I 

14 

2 

0 

205 

27 

1 

15 

3 

0 

30 

25 

1 

16 

2 

0 

210 

25 

2 

17 

2 

0 

35 

23 

2 

18 

2 

0 

215 

24 

1 

20 

3 

0 

40 

22 

1 

20 

2 

0 

220 

22 

2 

22 

2 

0 

45 

20 

1 

22 

2 

0 

225 

20 

2 

23 

1 

0 

2 

2 

2 

2 

50 

-18 

-24 

0 

230 

+18 

+25 

0 

55 

16 

+2 

25 

-1 

0 

235 

15 

-3 

26 

+1 

0 

60 

14 

2 

26 

1 

0 

240 

13 

2 

28 

3 

0 

65 

11 

3 

27 

1 

0 

245 

10 

3 

29 

1 

0 

70 

9 

2 

28 

1 

0 

250 

8 

2 

29 

0 

0 

i 

g 

_(-j 

75 

7 

m 

29 

0 

255 

5 

30 

0 

q 

—j 

3 

Q 

80 

4 

30 

0 

260 

+  2 

30 

0 

85 

-  1 

3 

30 

0 

0 

265 

0 

2 

30 

0 

0 

90 

+  1 

2 

30 

0 

0 

270 

-  3 

3 

30 

0 

0 

95 

4 

3 

30 

0 

0 

275 

5 

2 

30 

0 

0 

2 

0 

3 

-1 

100 

+  6 

-30 

0 

280 

-  8 

+29 

0 

105 

9 

+3 

29 

+1 

0 

285 

10 

-2 

28 

—1 

0 

110 

12 

3 

28 

1 

0 

290 

13 

3 

27 

1 

0 

115 

14 

2 

27 

1 

0 

295 

15 

2 

26 

1 

0 

120 

16 

2 

26 

1 

0 

300 

17 

2 

24 

2 

0 

125 

19 

3 

24 

2 

0 

305 

19 

2 

23 

1 

0 

130 

21 

2 

23 

1 

0 

310 

21 

2 

21 

2 

0 

135 

23 

2 

21 

2 

0 

315 

23 

2 

19 

2 

0 

140 

25 

2 

19 

2 

0 

320 

24 

1 

17 

2 

0 

145 

26 

1 

16 

3 

0 

325 

25 

1 

15 

2 

0 

2 

2 

2 

2 

150 

+28 

-14 

0 

330 

-27 

+13 

0 

155 

29 

+1 

11 

+3 

0 

335 

28 

-1 

10 

-3 

0 

160 

30 

1 

9 

2 

0 

340 

28 

0 

8 

2 

0 

165 

30 

0 

6 

3 

0 

345 

29 

-1 

6 

2 

0 

170 

31 

+1 

3 

3 

0 

350 

29 

0 

3 

3 

0 

175 

31 

0 

-  1 

2 

0 

355 

29 

0 

+  1 

2 

0 

180 

+31 

0 

+  2 

+3 

0 

360 

-29 

0 

-  2 

-3 

0 

TABLE    IV.—Gmtinued. 

I'KIMTKIIATIMNS  OF  TIIK  t'O-OKDINATKS  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT   XVI 

ARGUMENT  XVII. 

Arg. 

t 

Diff. 

1, 

Diff. 

Ei 

Arg. 

ft 

Diff. 

« 

Diff. 

& 

o 

0 

0 

+  113 

+    4 

+2 

0 

-103 

-  16 

-9 

5 

113 

0 

-    6 

-10 

5 

102 

+I 

94 

~* 

10 

119 

-  i 

15 

1 

2 

10 

99 

33 

• 

2 

15 

110 

9 

25 

10 

15 

96 

49 

• 

90 

108 

1 

34 

1 

90 

92 

50 

- 

1 

104 

4 

43 

95 

87 

57 

7 

30 

100 

4 

59 

+1 

30 

89 

64 

7 

-1 

35 

96 

ft 

61 

35 

76 

71 

7 

40 

89 

8 

69 

0 

40 

69 

7 

78 

7 

0 

45 

83 

8 

76 

1 

45 

62 

7 

83 

1 

7 

7 

8 

* 

50 

+  76 

-  83 

0 

50 

-54 

-  88 

0 

55 

68 

~  • 

89 

-  8 

55 

46 

+8 

93 

~* 

60 

60 

8 

96 

a 

-1 

60 

38 

96 

1 

+1 

65 

59 

8 

100 

1 

65 

99 

99 

1 

70 

43 

* 

104 

4 

1 

70 

90 

101 

9 

1 

75 

34 

I 

107 

1 

75 

11 

103 

-3 

80 

94 

10 

110 

* 

2 

80 

-    9 

103 

0 

1 

85 

14 

10 

111 

1 

85 

+    7 

103 

0 

90 

+    5 

B 

119 

~  l 

2 

90 

16 

109 

+  1 

2 

96 

-    5 

10 

119 

0 

95 

95 

101 

1 

10 

+  1 

B 

I 

100 

-  15 

-111 

3 

100 

+  34 

-  96 

2 

in:, 

95 

-10 

109 

+  9 

105 

49 

+8 

95 

+1 

110 

34 

107 

9 

3 

110 

50 

8 

91 

4 

2 

in 

43 

103 

4 

115 

58 

8 

86 

5 

m 

59 

99 

4 

3 

120 

66 

8 

81 

* 

2 

U6 

61 

94 

I 

125 

73 

7 

75 

130 

69 

88 

8 

3 

130 

79 

8 

68 

2 

UB 

77 

8 

89 

8 

135 

85 

6 

61. 

140 

84 

7 

75 

7 

3 

140 

90 

' 

54 

7 

3 

145 

90 

a 

68 

7 

145 

94 

4 

46 

8 

1 

8 

.4 

8 

150 

-96 

-60 

3 

150 

+  96 

-  38 

2 

155 

100 

51 

+  9 

155 

101 

* 

99 

+» 

160 

105 

49 

9 

3 

160 

103 

3 

20 

B 

2 

165 

106 

33 

9 

165 

104 

1 

11 

9 

170 

110 

24 

* 

2 

170 

105 

+1 

_     a 

9 

2 

175 

119 

14 

10 

175 

104 

—1 

+    7 

9 

180 

-113 

~ 

•    4 

+  10 

-2 

180 

+103 

-I 

+  16 

** 

+2 

180°  are  to  be  subtracted  from  the  Arguments  >  180°,  and  Si,  n,  and  d  to  be  taken  with  the  reversed  iign. 

• 

10 


TABLE    IV  .—Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  XVIII. 

ARGUMENT  XIX. 

Arg. 

fi 

Diff. 

% 

Diff. 

?i 

Arg. 

£1 

Diff. 

1l 

Diff. 

Ci 

o 

o 

0 

+43 

+  5 

0 

0 

+29 

+14 

-1 

10 

41 

-3 

12 

+7 

0 

10 

26 

-8 

18 

+4 

-1 

20 

39 

2 

19 

7 

0 

20 

22 

4 

22 

4 

0 

30 

35 

4 

26 

7 

0 

30 

17 

6 

26 

4 

0 

40 

30 

6 

31 

6 

0 

40 

12 

5 

28 

2 

0 

50 

24 

6 

36 

5 

0 

50 

7 

6 

30 

+2 

+1 

60 

17 

7 

40 

4 

0 

60 

+  1 

6 

30 

0 

1 

70 

10 

7 

42 

2 

0 

70 

-  5 

6 

30 

0 

1 

80 

+  3 

7 

43 

+1 

0 

80 

10 

5 

20 

-1 

2 

90 

-  5 

8 

43 

0 

0 

90 

15 

5 

27 

2 

2 

7 

-1 

5 

3 

100 

-12 

+42 

0 

100 

-20 

+24 

+2 

110 

19 

-7 

39 

-3 

0 

HO 

24 

-4 

21 

-3 

2 

120 

26 

7 

35 

4 

0 

120 

28 

4 

17 

4 

2 

130 

31 

5 

30 

5 

0 

130 

30 

2 

12 

6 

2 

140 

36 

5 

24 

6 

0 

140 

32 

2 

7 

6 

2 

150 

39 

3 

17 

7 

0 

150 

33 

-1 

+  2 

5 

1 

160 

42 

3 

10 

7 

0 

160 

33 

0 

-  4 

6 

1 

170 

43 

-1 

+  3 

7 

0 

170 

31 

+2 

9 

5 

1 

180 

-43 

0 

-  5 

-8 

0 

180 

-29 

+2 

-14 

-5 

+1 

ARGUMENT  XX. 

ARGUMENT  XXI. 

ARGUMENT  XXII. 

Arg. 

fit 

1)1 

fi 

Arg. 

Si 

% 

& 

Arg. 

& 

»h 

fi 

o 

o 

o 

0 

-27 

-  4 

0 

0 

+25 

+  1 

0 

0 

-24 

+10 

-8 

10 

26 

9 

0 

10 

24 

-  3 

0 

10 

21 

14 

8 

20 

24 

13 

0 

20 

24 

8 

0 

20 

17 

18 

8 

30 

21 

.      17 

0 

30 

22 

12 

0 

30 

13 

21 

7 

40 

18 

21 

0 

40 

20 

16 

0 

40 

9 

23 

7 

50 

14 

23 

0 

50 

17 

19 

0 

50 

-  4 

25 

6 

60 

10 

25 

•0 

60 

13 

22 

0 

60 

+  1 

26 

5 

70 

-  5 

27 

0 

70 

10 

24 

0 

70 

6 

26 

3 

80 

0 

27 

0 

80 

6 

26 

0 

80 

10 

25 

2 

90 

+  4 

27 

0 

90 

+  1 

26 

0 

90 

15 

23 

-1 

100 

+  9 

-26 

0 

100 

-  3 

-26 

0 

100 

+19 

+21 

+1 

110 

13 

24 

0 

110 

7 

25 

0 

110 

22 

19 

2 

120 

17 

21 

0 

120 

11 

24 

0 

120 

25 

15 

4 

130 

21 

18 

0 

130 

15 

21 

0 

130 

26 

11 

5 

140 

23 

14 

0 

140 

•  18 

18 

0 

140 

28- 

7 

6 

150 

25 

10 

0 

150 

21 

14 

0 

150 

28 

+  3 

7 

160 

27 

-  5 

0 

160 

23 

10 

0 

160 

27 

-  2 

8 

170 

27 

0 

0 

170 

24 

6 

0 

170 

26 

6 

8 

ISO 

+27 

+  4 

0 

180 

-25 

-  1 

0 

•     180 

+24 

-10 

+8 

180°  are  to  be  subtracted  from  the  Arguments  >  180°,  and  |i,  iji,  and  ti  to  be  taken  with  the  reversed  sign. 

75 


TABLE    IV.—  Continued. 

P1.RTURBATIONS  OF  THE  CO-OUDINATES  IN  t  NITS  OF  THE  SIXTH  DECIMAL. 

AUt.rMI.N  I'    XXIII 

AK'.I'M!  NT    XXIV. 

ARGUMENT  XXV. 

Arg. 

6 

1i 

& 

Arg. 

fi 

1i 

Ci 

Arg. 

k 

«h 

fi 

o 

0 

0 

0 

-aa 

-  3 

-i 

0 

+30 

-4 

+2 

0 

-19 

+  1 

0 

10 

23 

+  3 

i 

10 

30 

4 

1 

10 

19 

4 

0 

30  . 

ai 

6 

-i 

30 

18 

4 

+1 

30 

18 

7 

0 

30 

90 

10. 

0 

30 

1C 

3 

0 

30 

16 

10 

0 

40 

18 

i:t 

0 

40 

14 

3 

-1 

40 

14 

13 

0 

50 

15 

16 

0 

50 

11 

2 

2 

50 

13 

15 

0 

60 

13 

18 

0 

60 

8 

1 

2 

60 

9 

17 

0 

70 

9 

30 

+1 

70 

+  4 

-1 

3 

TO 

6 

18 

0 

80 

1 

B 

1 

80 

0 

0 

80 

-  3 

19 

0 

90 

-  1 

23 

1 

90 

-  3 

+1 

90 

+  1 

19 

0 

100 

+  3 

+22 

+1 

100 

-  7 

+1 

-4 

100 

+  4 

+19 

0 

110 

6 

81 

1 

110 

10 

2 

110 

7 

18 

0 

m 

10 

20 

2 

120 

13 

3 

120 

10 

16 

0 

no 

13 

18 

2 

130 

16 

3 

130 

13 

14 

0 

MO 

16 

15 

2 

140 

18 

4 

140 

15 

13 

0 

150 

18 

12 

2 

150 

19 

4 

150 

17 

9 

0 

160 

30 

9 

1 

160 

90 

4 

3 

160 

18 

6 

0 

170 

22 

1 

1 

170 

21 

4 

3 

170 

1!» 

+  3 

0 

IfO 

-•--.' 

+  3 

+1 

180 

-90 

+  4 

-9 

1-0 

+1!) 

-  1 

0 

ARGUMENT  XXVI. 

ARGUMENT  XXVII. 

ARGUMENT  XXVIII. 

Arg. 

fi 

•h 

fi 

Arg. 

ft 

1l 

fi 

Arg. 

t 

fli 

& 

o 

O 

o 

0 

+19 

+13 

0 

0 

+16 

+11 

+3 

0 

-15 

+  5 

+1 

10 

21 

9 

0 

10 

14 

7 

3 

10 

14 

8 

1 

80 

23 

6 

0 

20 

12 

+  2 

3 

20 

13 

11 

1 

30 

34 

+  2 

0 

30 

10 

-  2 

2 

30 

13 

14 

+1 

40 

34 

-  2 

0 

40 

7 

7 

2 

40 

10 

16 

0 

50 

83 

6 

0 

50 

4 

11 

2 

50 

8 

18 

0 

60 

82 

10 

0 

60 

+  1 

15 

1 

60 

6 

19 

b 

70 

30 

13 

0 

70 

-  3 

19 

+1 

70 

-  3 

20 

0 

80 

17 

16 

0 

80 

6 

22 

0 

80 

0 

19 

- 

90 

14 

19 

0 

90 

9 

24 

0 

90 

+  2 

19 

100 

+11 

-21 

0 

100 

-11 

-35 

-1 

100 

+  5 

+18 

- 

110 

7 

22 

0 

110 

14 

96 

1 

110 

7 

16 

120 

+  3 

83 

0 

120 

16 

26 

2 

120 

9 

14 

130 

-  1 

23 

0 

130 

17 

25 

2 

130 

11 

11 

2 

140 

6 

22 

0 

140 

18 

24 

3 

140 

13 

8 

2 

150 

10 

20 

0 

150 

18 

21 

3 

150 

14 

5 

2 

160 

13 

18 

0 

160 

18 

19 

3 

160 

15 

+  2 

2 

170 

16 

16 

0 

170 

17 

15 

3 

170 

15 

-  3 

2 

180 

-19 

-13 

0 

180 

-16 

-11 

-3 

at 

+15           -  5 

-1 

180°  are  to  be  subtracted  from  the  Argument*  >  180°,  and  -,,  n,  and  ti  to  be  taken  with  the  rerersed  sign. 

TABLE    IV.—  Continued. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  XXIX. 

ARGUMENT  XXX. 

ARGUMENT  XXXI. 

Arg. 

£1 

1i 

& 

Arg. 

& 

fe 

& 

Arg. 

li 

« 

& 

o 

o 

o 

0 

+12 

+  1 

0 

0 

-8 

__l 

0 

0 

-7 

-1 

0 

10 

12 

-  1 

0 

10 

8 

2 

0 

10 

7 

2 

0 

20 

12 

3 

0 

20 

7 

3 

0 

20 

6 

3 

0 

30 

11 

5 

0 

30 

7 

5 

0 

30 

6 

4 

0 

40 

10 

7 

0 

40 

6 

6 

0 

40 

5 

5 

0 

50 

9 

9 

0 

50 

5 

7 

0 

50 

4 

6 

0 

60 

7 

10 

0 

60 

4 

8 

0 

60 

3 

6 

0 

70 

5 

11 

0 

70 

2 

8 

0 

70 

-2 

7 

0 

80 

3 

12 

0 

80 

-1 

8 

0 

80 

0 

7 

0 

90 

+  1 

12 

0 

90 

+1 

8 

0 

90 

+1 

7 

0 

100 

-  1 

-12 

-1 

100 

+2 

-8 

0 

100 

+2 

-6 

0 

110 

3 

12 

1 

110 

3 

8 

0 

110 

3 

6 

0 

120 

5 

11 

1 

120 

4 

7 

0 

120 

4 

5 

0 

130 

7 

10 

1 

130 

5 

6 

0 

130 

5 

5 

0 

140 

9 

9 

1 

140 

6 

5 

0 

140 

6 

4 

0 

150 

10 

7 

1 

150 

7 

4 

0 

150 

7 

3 

0 

160 

11 

5 

-1 

160 

8 

2 

0 

160 

7 

-2 

0 

170 

12 

3 

0 

170 

8 

-1 

0 

170 

7 

0 

0 

180 

-12 

-  1 

0 

180 

+8 

+1 

0 

180 

+7 

+1 

0 

ARGUMENT  XXXII. 

ARGUMENT  XXXIII. 

ARGUMENT  XXXIV. 

Arg. 

fi 

fli 

t, 

Arg. 

li 

•Ji 

& 

Arg. 

& 

•ni 

& 

o 
0 

+4 

-5 

0 

o 
0 

+3 

0 

0 

O 

0 

+3 

0 

0 

10 

5 

4 

0 

10 

3 

0 

0 

10 

3 

+1 

0 

20 

6 

3 

0 

20 

3 

_j 

0 

20 

3 

i 

0 

30 

6 

2 

0 

30 

3 

1 

0 

30 

2 

2 

0 

40 

7 

-1 

0 

40 

3 

2 

0 

40 

2 

2 

0 

50 

7 

0 

0 

50 

2 

2 

0 

50 

2 

2 

0 

60 

7 

+1 

0 

60 

2 

3 

0 

60 

1 

3 

0 

70 

6 

2 

0 

70 

1 

3 

0 

70 

+1 

3 

0 

80 

6 

3 

0 

80 

+1 

3 

0 

80 

0 

3 

0 

90 

5 

4 

0 

90 

0 

3 

0 

90 

0 

3 

0 

100 

+4 

+5 

0 

100 

0 

-3 

0 

100 

-1 

+3 

0 

110 

3 

5 

0 

110 

_j 

3 

0 

110 

1 

3 

0 

120 

2 

6 

0 

120 

1 

3 

0 

120 

2 

2 

0 

130 

+1 

6 

0 

130 

2 

3 

0 

130 

2 

2 

0 

140 

0 

6 

0 

140 

2 

2 

0 

140 

3 

2 

0 

150 

-1 

6 

0 

150 

3 

2 

0 

150 

3 

1 

0 

160 

2 

6 

0 

160 

3 

1 

0 

160 

3 

+1 

0 

170 

3 

5 

0 

170 

3 

-1 

0 

170 

3 

0 

0 

180 

-4 

+5 

0 

180 

-3 

0 

0 

180 

-3 

0 

0 

180°  are  to  be  subtracted  from  the  Arguments  >  180°,  and  I,,  n,  and  ti  to  be  taken  with  the  reversed  sign. 

77 


TABLE    IV.—  CiHifini','1. 

1'I.KTrRBATIOXS  OF  THK  CO-ORDIXATKS  IX  l.NITS  OF  THE  SIXTH  DECIMAL. 

ARI;UMI:M   xxxv. 

ARGUMKNT   XXXVI 

AKtifMKNT    XXXVII. 

6 

li 

f, 

AIR. 

£i 

<h 

& 

A,. 

ft      ' 

li 

& 

o 

o 

o 

0 

-3    ' 

+1 

0 

0 

-2 

0 

0 

0 

+2 

+  2 

-1 

10 

:t 

1 

0 

10 

2 

0 

0 

10 

2 

4 

0 

20 

3 

1 

0 

20 

2 

-1 

0 

30 

2 

6 

0 

30 

2 

1 

0 

30 

2 

1 

0 

30 

2 

7 

0 

40 

2 

1 

0 

40 

2 

1 

0 

40 

2 

9 

0 

50 

2 

+1 

0 

50 

1 

2 

0 

50 

2 

10 

0 

60 

2 

0 

0 

60 

1 

2 

0 

60 

2 

11 

0 

70 

1 

0 

0 

70 

-1 

2 

0 

70 

1 

11 

+1 

80 

-1 

0 

0 

80 

0 

2 

0 

80 

1 

12 

90 

0 

0 

0 

90 

0 

2 

0 

90 

+1 

11 

100 

0 

0 

0 

100 

+1 

-2 

0 

100 

0 

-HI 

+ 

110 

+1 

- 

0 

110 

1 

2 

0 

110 

0 

10 

120 

1 

0 

120 

1 

2 

0 

120 

-1 

9 

130 

1 

0 

130 

2 

2 

0 

130 

1 

7 

140 

2 

0 

140 

2 

1 

0 

140 

1 

6 

in 

2 

0 

150 

2 

1 

0 

150 

2 

4 

160 

2 

0 

160 

2 

-1 

0 

160 

2 

+  2 

170 

2 

0 

170 

2 

0 

0 

170 

2 

0 

1 

180 

+3 

- 

0 

180 

a 

0 

0 

180 

-8 

-  3 

+1 

ARGUMENT  XXXVIII. 

ARGUMENT  XXXIX. 

.ARGUMENT  XL. 

Arg. 

ft 

fl 

& 

Aig. 

t 

li 

& 

Arg. 

ft 

It 

& 

o 

o 

o 

0 

-2 

+4 

0 

0 

-2 

-2 

+2 

0 

-2 

0 

0 

20 

3 

4 

0 

23 

2 

-1 

1 

20 

2 

-1 

0 

40 

4 

3 

0 

40 

3 

0 

1 

40 

1 

1 

0 

60 

4 

2 

0 

60 

3 

+1 

+1 

60 

-1 

2 

0 

80 

3 

+1 

0 

80 

2 

1 

0 

80 

0 

2 

0 

100 

3 

-1 

+1 

100 

2 

2 

0 

100 

+1 

2 

0 

120 

-2 

1 

1 

120 

-1 

3 

-1 

120 

1 

1 

0 

140 

0 

3 

+1 

140 

0 

3 

1 

140 

2 

-1 

0 

160 

+1 

4 

0 

160 

+1 

3 

1 

160 

2 

0 

0 

180 

+2 

-4 

0 

180 

+2 

+2 

-8 

l-u 

+2 

0 

0 

180°  are  to  be  subtracted  from  the  Arguments  >  180°,  and  li,  ui,  and  ft  to  be  taken  with  the  reversed  sign. 

78 


TABLE    IV.—  Concluded. 

PERTURBATIONS  OF  THE  CO-ORDINATES  IN  UNITS  OF  THE  SIXTH  DECIMAL. 

ARGUMENT  XLI.                                ARGUMENT  XLII.                              ARGUMENT  XLIII. 

Arg. 

Ii 

'ji 

&              Arg.             & 

^i              £1              Arg. 

&           ii          Si 

o 

o 

0 

-1 

0 

0                 0-1 

+20                  0 

-100 

20 

1 

+1 

0                20               0 

2               0                20 

100 

40 

-1 

i 

0                40               0 

2              0                40 

-1             +1              0 

60 

0 

i 

0                60             +1 

2              0                60 

010 

80 

0 

i 

0                80                1 

1               0                80 

010 

100 

0 

i 

0               100               2 

+1               0              100 

010 

120 

+1 

i 

0               120               2 

0              0              120 

+110 

140 

1 

+1 

0               140               2 

-1               0              140 

1             +1               0 

160 

1 

0 

0               160                1 

1               0              160 

100 

180 

+1 

0 

0              180            +1 

-2              0              180 

+100 

ARGUMENT  XLIV. 

ARGUMENT  XLV. 

Arg. 

fl 

%                       £i 

Arg.                      {t 

*ii                 Si 

0 

o 

0 

-1 

+1                        0 

0                        0 

0                        0 

20 

1 

0                        0 

20                     -1 

0                        0 

40 

1 

0                        0 

40                        1 

-1                       0 

60 

-1 

0                       0 

60                        1 

1                        0 

80 

0 

0                        0 

80                       1 

2                       0 

100 

0 

0                       0 

100                       1 

2                      0 

120 

0 

0                       0 

120                       1 

2                      0 

140 

0 

-1                       0 

140                    -1 

1                        0 

160 

+1 

1                        0 

160                       0 

-1                       0 

180 

+1 

-1                        0 

180                        0 

0                       0 

180°  are  to  be  subtracted  from  the  Arguments  >  180°,  and  ii,  n,  and  Ci  to  be  taken  with  the  reversed  sign. 

TABLE    V. 

LOGARITHMS    Fou    UF.FF.KIM  \(.    THK    I'KIMTUHATIONS   TO   THE   EQUATOR. 

Mean  Equinox  of  the  beginning  of  the  Tear. 

Yean. 

«o«  (*i  *) 

o»(jnx) 

«•(»!») 

«*  (1») 

coi  (yi  jf) 

«»  (*iy) 

cot  (»i«) 

«o«(jn*) 

«(*.) 

I-.v.'/J      '  .  •-.•:ii. 

9.423945* 

8.944771 

•  <M3 

9^(66907 

9.400926N 

-.I...7..-./, 

9^25327 

MMM 

I-.YI 

9.424:KT./« 

-.''44808 

•Ml...  I,, 

9.966680 

'J.400892M 

8.167022n 

MSfSBt 

••.•,-.:•'-! 

l-.,  i 

•a 

9.42471  >7  /i 

&MMM 

MMOT 

9.966852 

9.400858M 

-.H.I-Ju./i 

9.425243 

y«*iooy^w 

l-;,:, 

MM068N 

8.944t2l5 

'.'.117012 

gUK6-.'l 

MOOK.'4'i 

8.161  466n 

9.425201 

9.9tK«Ki2 

i-  I  B 

M9M6BN 

17345 

9.9667116 

9.400791  n 

8.156674M 

9.425159 

9.983iN« 

I-.-.7 

Jl7:i 

9.423.S4*n 

8.943844 

•'.117,  .77 

9.966766 

9.400757» 

8.155432M 

9.425117 

9.964000 

B81 

9.426227n 

8.943658 

MMOM 

9.966740 

9.400723n 

8.152!l9l'i 

9.495075 

9.964004 

1H.V.I 

•i-.". 

9.4266C6n 

8.943473 

9.448341 

'1712 

9.400669» 

8.1501  42n 

9.425033 

9.084C06 

1-1,  i  /.' 

ii.'i-  1 

9.426964n 

8.943266 

:i.  11-673 

9.966664 

9.400656n 

8.147263n 

9.4241KH) 

9.964011 

1961 

9.427362n 

8^4:ili»i 

:i.li 

9.966056 

9.400622» 

8.144356n 

'.'.l-T'l- 

9.964015 

M,-J 

•i.i-.c7r  « 

8.942914 

9.4J 

9.966628 

9.400568n 

-.11111  — 

9.424905 

9.984019 

1-.,:: 

-M12 

9.4981  17n 

8.94  V728 

9.44!>666 

9.966600 

9.400554n 

8.136472»» 

9.424863 

9.964C23 

•MB 

'.'.•'-1984 

9.438494n 

8.942M1 

9.44 

9.»H 

9.40U.V.'l;i 

8.135514n 

9.4VM--"' 

9.964C27 

i-.,-, 

9.981956 

9.42867  in 

8.942355 

9.450326 

9.966544 

9.400487» 

8.132546n 

9.424778 

9.984031 

i-.-, 

-1938 

9.429247n 

-."r.'h,- 

!U.. 

9.966516 

9.400454n 

8.129549n 

9.424735 

9.934035 

1667 

9.981-.MKI 

9.429623n 

8.941981 

9.4.V)!»e6 

9.f!664rt6 

9.400420n 

-.I-J.V.'I" 

9.424693 

9.984039 

i-.,-  /; 

-1*79 

9.429999* 

8.941794 

9.451315 

9^66459 

9.400387n 

8.123466n 

9.424650 

9.984042 

tM 

9.961844 

9.430374n 

-.•'ll«,  7 

9.4:>1G44 

•i.!W6431 

9.400353n 

8.120409n 

9.424608 

9.984(!46 

1870 

1316 

9.430749n 

8.941420 

an 

9.966403 

9.400320» 

8.117336n 

9.424565 

9.984050 

1871 

9.981788 

•1.4:11  134n 

8.941233 

9.4r>2301 

'.i.'.  '66375 

:M  ».-.•-.,« 

8.11424  l/< 

9.45M.V.".' 

9.984064 

i  -:•.•/; 

9.981760 

9.431498* 

6.941045 

5)89 

9.!«6346 

9.4002.->:t;» 

-.11  11  1  I// 

9.424479 

9.964068 

1873 

9.9817:tt 

n.4-.U672» 

8.940868 

9.4.-,*  157 

9.966318 

9.40021  On 

8.107956n 

9.424437 

9.964C62 

1874 

9.981704 

9.432--'  .|:.;» 

8.940670 

'.M.-.3284 

9.966290 

9.400166n 

8.104794n 

9.424  394 

9.984C66 

1875 

9.981676 

9.432618n 

8.940463 

•i..|r,36l2 

9.966262 

9.400152n 

8.101610n 

9.424351 

9.984070 

i-;.;/,' 

ncir 

9.438!)!iln 

8.940205 

9.453-139 

9.966233 

9.4001  19n 

8.0963(*7» 

9.424308 

9.984073 

1677 

9.981619 

9.43X)64n 

8.940107 

9.454266 

9.966205 

9.400065n 

8.0951  34»» 

9.424265 

9.964077 

1-7- 

9.961  .V>1 

9.433736n 

8.939919 

9.966177 

9.400052n 

8.091878n 

9.424222 

9.964C81 

!-:•> 

9.981563 

9.434106n 

8^3!>7:il 

9.454918 

9.966149 

9.400019n 

8.08NVI7H 

9.424179 

9.964085 

i  --,,/; 

9.981534 

9.43447;>n 

8.93!t:.i:i 

9.455244 

•1.966120 

9.399986n 

8.085275H 

9.424136 

9.984068 

1881 

9.961506 

9.4:H-:.u;t 

U9HH 

9.455.-.70 

9.966092 

9.399952»» 

8.081923n 

9.424093 

.,    .„,  ._, 

1--  .' 

9.981478 

9.43S»lu 

8.939167 

:i.l.Vj895 

9.!»66063 

9.39991  9n 

8.078529n 

9.424050 

UK6 

l--:t 

-1450 

9^36Ti!M» 

9.456220 

9.966'  KIT, 

9.3996S6n 

8.0751  10n 

9.424007 

9.964100 

I  —  I  /( 

1  lv!l 

9.4350611 

MMM 

9.456545 

9^)66006 

9.39»853n 

8.07171  in 

9.423TG4 

94)84103 

l-v-. 

9.981393 

9^36:Ciln 

8.938632 

!'.  156869 

9.965978 

rt.;eii»6i9n 

8.C6fti65n 

9.423H21 

9.984107 

1--., 

9.981364 

9.43670(W 

8.936413 

:i.i:,7193 

9.965949 

9.399786n 

8.064795* 

9.423878 

9.964111 

1—  7 

9.961336 

9.437069n 

8.938224 

9.457517 

9.965!)21 

9.399753n 

8.C61302n 

9.423^:1". 

1115 

1888  B 

-1307 

9.437438n 

8.938035 

9.457841 

9.965892 

9.399720W 

8.057762n 

9.423791 

9.984119 

l-i 

-1279 

9.437807n 

8.937846 

9.456164 

9.965864 

9.399687n 

8.054  l!i*i 

9.423748 

9.984123 

I-MI 

-1250 

I178N 

8.937657 

9.458487 

9.965835 

9.3!W654n 

8.050612n 

9.423704 

9.964127 

l-.ll 

9.96)223 

9.438543n 

8.937468 

9.456610 

9.965806 

9.3!>n621n 

8.046982R 

9.423661 

9.964131 

LMtl 

'.i.!i*1193 

9^3«)10n 

Mmn 

9.459133 

9.965777 

9.399586H 

8.043323n 

9.423617 

9.964134 

I8H 

-1165 

9.4:»0277n 

8.937089 

9.459455 

9.965749 

9.399555n 

8.039652n 

9.423573 

9.984138 

1894 

9.961136 

9.439644/1 

8.936*19 

9.4511777 

9.965720 

9.399522n 

8.035950n 

9.42352!! 

9.964142 

!-•'•, 

9.981108 

9.44001  in 

8JKK709 

9.460099 

9.965691 

9.399489» 

8.032211* 

9.423485 

9.984146 

1-N,/.' 

9.961079 

9.440377n 

8.936S19 

9.460420 

9.965662 

9.399456» 

8.028449n 

9.423442 

9.984149 

1897 

9.961051 

9.440743n 

8^36329 

9.460741 

9.965634 

9.399423W 

8.024650K 

9.423398 

9.984153 

1-,- 

9.981022 

9.441  108H 

8.936139 

9.461061 

9.965605 

9.399390n 

8.020817n 

9.423355 

9.984157 

1899 

9.980993 

9.441474K 

8.935949 

9.461  :i-j 

9.965576 

9.399357n 

8.016950n 

9.42331  1 

9.994161 

'.l.'.MIIMit 

!).441^:!!bi 

8.93T.7.-.- 

9.46  17i  )2 

!i.'.  *>:.:>  17 

!>.:!•.  «i32T>n 

8.013046n 

!'.423268 

9.984164 

80 


TABLE    VI. 

CONSTANTS   FOR  THE   EQUATOR. 

Equator  and  mean  Equinox  at  the  beginning  of  the  Year. 

Tears. 

A' 

B' 

C' 

log  sin  a. 

log  sin  b. 

log  sin  c. 

O        1         It 

O        1          II 

O         1          II 

1852  B 

105  27  14.0 

16  46  17.2 

356  49  20.7 

9.998310 

9.985785 

9.425995 

1853 

105  28    3.8 

16  47    4.6 

356  50  31.7 

9.998311 

9.985787 

9.425945 

1854 

105  28  53.6 

16  47  52.0 

356  51  42.7 

9.998313 

9.985790 

9.425895 

1855 

105  29  43.5 

16  48  39.2 

356  52  53.8 

9.998314 

9.985792 

9.425844 

1856  B 

105  30  33.4 

16  49  26.8 

356  54    5.0 

9.998316 

9.985794 

9.425794 

1857 

105  31  23.2 

16  50  14.2 

356  55  16.1 

9.998317 

9.985797 

9.425744 

1858 

105  32  13.0 

16  51     1.6 

356  56  27.1 

9.998319 

9.985799 

9.425694 

1859 

105  33    2.9 

16  51  49.0 

356  57  38.2 

9.998320 

9.985801 

9.425644 

1860  B 

105  33  52.8 

16  52  36.5 

356  58  49.5 

9.998321 

9.985804 

9.425593 

1S61 

105  34  42.6 

16  53  23.8 

357    0    0.6 

9.998323 

9.9858C6 

9.425543 

1862 

105  35  32.4 

16  54  11.2 

357    1  11.7 

9.998324 

9.985808 

9.425493 

1863 

105  36  22.2 

16  54  58.6 

357    2  22.9 

9.998326 

9.985811 

9.425443 

1864  B 

105  37  12.2 

16  55  46.1 

357    3  34.2 

9.998327 

9.985813 

9.425302 

1865 

105  38    2.0 

16  56  33.5 

357    4  45.4 

9.998329 

9.985815 

9.425342 

1866 

105  38  51.8 

16  57  20.9 

357    5  56.5 

9.998330 

9.985818 

9.425292 

1867 

105  39  41.6 

16  58    8.2 

357    7    7.7 

9.998331 

9.985820 

9.425242 

•    1868  B 

105  40  31.6 

16  58  55.8 

357    8  19.1 

9.998333 

9.985822 

9.425192 

1869 

105  41  21.4 

16  59  43.1 

357    9  30.3 

9.998334 

9.985825 

9.425142 

1870 

105  42  11.2 

17    0  30.5 

357  10  41.5 

9.998336 

9.985827 

9.425092 

1871 

105  43    1.0 

17    1  17.9 

357  11  52.7 

9.998337 

9.985829 

9.425042 

1872  B 

105  43  50.9 

17    2    5.4 

357  13    4.1 

9.998339 

9.985831 

9.424991 

1873 

105  44  40.7 

17    2  52.8 

357  14  15.4 

9.998340 

9.985834 

9.424941 

1874 

105  45  30.5 

17    3  40.2 

357  15  26.6 

9.998342 

9.985836 

9.424891 

1875 

105  46  20.3 

17    4  27.6 

357  16  37.9 

9.998343 

9.985838 

9.424841 

1876  B 

105  47  10.3 

17    5  15.1 

357  17  49.3 

9.998344 

9.985840 

9.424791 

1877 

105  48    0.1 

17,    6    2.5 

357  19    0.6 

9.998346 

9.985843 

9.424741 

1878 

105  48  49.9 

17    6  49.8 

357  20  11.9 

9.998347 

9.985845 

9.424691 

1879 

105  49  39.7 

17    7  37.2 

357  21  23.2 

9.998349 

9.985847 

9.424641 

1880  B 

105  50  29.7 

17    8  24.7 

357  22  34.7 

9.998350 

9.985849 

9.424591 

1881 

105  51  19.5 

17    9  12.1 

357  23  46.0 

9.998352 

9.985852 

9.424541 

1882 

105  52    9.3 

17    9  59.5 

357  24  57.3 

9.998353 

9.985854 

9.424491 

1883 

105  52  59.1 

17  10  46.9 

357  26    8.7 

9.998354 

9.985856 

9.424441 

1884  B 

105  53  49.0 

17  11  34.4 

357  27  20.2 

9.998356 

9.985858 

9.424391 

1885 

105  54  38.8 

17  12  21.8 

357  28  31.6 

9.998357 

9.985660 

9.424341 

1886 

105  55  28.6 

17  13    9.1 

357  29  42.9 

9.998359 

9.985863 

9.424291 

1887 

105  56  18.4 

17  13  56.5 

357  30  54.3 

9.998360 

9.985865 

9.424241 

1888  B 

105  57    8.4 

17  14  44.0 

357  32    5.9 

9.998361 

9.985867 

9.424191 

1889 

105  57  58.2 

17  15  31.4 

357  33  17.3 

9.998363 

9.985869 

9.424141 

1890 

105  58  48.0 

17  16  18.8 

357  34  28.7 

9.998364 

9.985871 

9.424C91 

1891 

105  59  37.8 

17  17    6.2 

357  35  40.2 

9.998366 

9.985874 

9.424041 

1892  B 

106    0  27.7 

17  17  53.7 

357  36  51.8 

9.998367 

9.985876 

9.423991 

1893 

106    1  17.5 

17  18  41.1 

357  38     3.2 

9.998369 

9.985878 

9.42394] 

1894 

106    2    7.3 

17  19  28.5 

357  39  14.7 

9.998370 

9.985880 

9.423891 

1895 

106    2  57.2 

17  20  15.9 

357  40  26.2 

9.998371 

9.985882 

9.423841 

1896  B 

106    3  47.1 

17  21     3.4 

357  41  37.8 

9.998373 

9.985884 

9.423792 

1897 

106    4  36.9 

17  21  50.8 

357  42  49.4 

9.998374 

9.985886 

9.423742 

1898 

106    5  26.7 

17  22  38.1 

357  44    0.9 

9.998376 

9.985888 

9.423692 

1899 

106    6  16.5 

17  23  25.5 

357  45  12.4 

9.998377 

9.985890 

9.423642 

1900  B 

106    7    6.5 

17  24  13.0 

357  46  24.1 

9.998379 

9.985893 

9.423592 

OF  THE 

UNIVERSITY 


CALIFORNIA 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 

ASTRCNDMY    LIBRARY 


^5«rVS*2?  ^'•r!^ji^vS?«^i 


•Sl    ^  I  «Ct  4 


I2SHKR 


•?  <.»/'•.;  "V  <?v  'SpJ-'^P  f]''<*\     Ve   *v'  r    ;V;,7.f.^l^~*5^Xr*.Vr.'  w  v«5S^sf;-    r 

*n  3Nf^<S8^'.;   -- 

?£ 


